From 16c404a372198143aa944ff580dd5816619000c3 Mon Sep 17 00:00:00 2001 From: Shuhei Ohno Date: Thu, 30 Nov 2023 06:30:32 +0900 Subject: [PATCH] Fix Template --- .../workflows/{documentation.yml => CI.yml} | 104 ++-- .github/workflows/CompatHelper.yml | 16 + .github/workflows/TagBot.yml | 31 ++ .gitignore | 1 + Project.toml | 16 +- README.md | 3 +- developer.ipynb | 492 +++++++++++------- docs/Project.toml | 1 + docs/jmd2md.jl | 20 + docs/src/HarmonicOscillator.md | 52 +- docs/src/HydrogenAtom.md | 120 ++--- docs/src/InfinitePotentialWell.md | 10 +- docs/src/MorsePotential.md | 112 ++-- .../src/assets/fig/HarmonicOscillator_5_1.png | Bin 59935 -> 60130 bytes src/Antiq.jl | 2 +- src/HarmonicOscillator.jl | 2 +- test/HarmonicOscillator.jl | 4 +- 17 files changed, 599 insertions(+), 387 deletions(-) rename .github/workflows/{documentation.yml => CI.yml} (61%) create mode 100644 .github/workflows/CompatHelper.yml create mode 100644 .github/workflows/TagBot.yml create mode 100644 docs/jmd2md.jl diff --git a/.github/workflows/documentation.yml b/.github/workflows/CI.yml similarity index 61% rename from .github/workflows/documentation.yml rename to .github/workflows/CI.yml index 2169ed4..ca6b92b 100644 --- a/.github/workflows/documentation.yml +++ b/.github/workflows/CI.yml @@ -1,40 +1,64 @@ -name: Documentation -on: - push: - branches: - - main - tags: ['*'] - pull_request: -concurrency: - # Skip intermediate builds: always. - # Cancel intermediate builds: only if it is a pull request build. - group: ${{ github.workflow }}-${{ github.ref }} - cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }} -jobs: - docs: - name: Documentation - runs-on: ubuntu-latest - permissions: - contents: write - statuses: write - steps: - - uses: actions/checkout@v3 - - uses: julia-actions/setup-julia@v1 - with: - version: '1' - - name: Configure doc environment - run: | - julia --project=docs/ -e ' - using Pkg - Pkg.develop(PackageSpec(path=pwd())) - Pkg.instantiate()' - - uses: julia-actions/julia-buildpkg@v1 - - uses: julia-actions/julia-docdeploy@v1 - env: - GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} - - run: | - julia --project=docs -e ' - using Documenter: DocMeta, doctest - using Antiq - DocMeta.setdocmeta!(Antiq, :DocTestSetup, :(using Antiq); recursive=true) - doctest(Antiq)' \ No newline at end of file +name: CI +on: + push: + branches: + - main + tags: ['*'] + pull_request: +concurrency: + # Skip intermediate builds: always. + # Cancel intermediate builds: only if it is a pull request build. + group: ${{ github.workflow }}-${{ github.ref }} + cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }} +jobs: + test: + name: Julia ${{ matrix.version }} - ${{ matrix.os }} - ${{ matrix.arch }} - ${{ github.event_name }} + runs-on: ${{ matrix.os }} + strategy: + fail-fast: false + matrix: + version: + - '1.0' + - '1.6' + - '1.7' + - 'nightly' + os: + - ubuntu-latest + arch: + - x64 + steps: + - uses: actions/checkout@v3 + - uses: julia-actions/setup-julia@v1 + with: + version: ${{ matrix.version }} + arch: ${{ matrix.arch }} + - uses: julia-actions/cache@v1 + - uses: julia-actions/julia-buildpkg@v1 + - uses: julia-actions/julia-runtest@v1 + docs: + name: Documentation + runs-on: ubuntu-latest + permissions: + contents: write + statuses: write + steps: + - uses: actions/checkout@v3 + - uses: julia-actions/setup-julia@v1 + with: + version: '1' + - name: Configure doc environment + run: | + julia --project=docs/ -e ' + using Pkg + Pkg.develop(PackageSpec(path=pwd())) + Pkg.instantiate()' + - uses: julia-actions/julia-buildpkg@v1 + - uses: julia-actions/julia-docdeploy@v1 + env: + GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} + - run: | + julia --project=docs -e ' + using Documenter: DocMeta, doctest + using Antiq + DocMeta.setdocmeta!(Antiq, :DocTestSetup, :(using Antiq); recursive=true) + doctest(Antiq)' diff --git a/.github/workflows/CompatHelper.yml b/.github/workflows/CompatHelper.yml new file mode 100644 index 0000000..cba9134 --- /dev/null +++ b/.github/workflows/CompatHelper.yml @@ -0,0 +1,16 @@ +name: CompatHelper +on: + schedule: + - cron: 0 0 * * * + workflow_dispatch: +jobs: + CompatHelper: + runs-on: ubuntu-latest + steps: + - name: Pkg.add("CompatHelper") + run: julia -e 'using Pkg; Pkg.add("CompatHelper")' + - name: CompatHelper.main() + env: + GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} + COMPATHELPER_PRIV: ${{ secrets.DOCUMENTER_KEY }} + run: julia -e 'using CompatHelper; CompatHelper.main()' diff --git a/.github/workflows/TagBot.yml b/.github/workflows/TagBot.yml new file mode 100644 index 0000000..2bacdb8 --- /dev/null +++ b/.github/workflows/TagBot.yml @@ -0,0 +1,31 @@ +name: TagBot +on: + issue_comment: + types: + - created + workflow_dispatch: + inputs: + lookback: + default: 3 +permissions: + actions: read + checks: read + contents: write + deployments: read + issues: read + discussions: read + packages: read + pages: read + pull-requests: read + repository-projects: read + security-events: read + statuses: read +jobs: + TagBot: + if: github.event_name == 'workflow_dispatch' || github.actor == 'JuliaTagBot' + runs-on: ubuntu-latest + steps: + - uses: JuliaRegistries/TagBot@v1 + with: + token: ${{ secrets.GITHUB_TOKEN }} + ssh: ${{ secrets.DOCUMENTER_KEY }} diff --git a/.gitignore b/.gitignore index 6c39b88..dcbb5ff 100644 --- a/.gitignore +++ b/.gitignore @@ -1,6 +1,7 @@ *.jl.*.cov *.jl.cov *.jl.mem +/Manifest.toml /docs/Manifest.toml /docs/build/ diff --git a/Project.toml b/Project.toml index 10ac33d..5e40c0a 100644 --- a/Project.toml +++ b/Project.toml @@ -1,18 +1,26 @@ name = "Antiq" uuid = "be6e5d0e-34a5-4c8f-af83-e1b5389203d8" authors = ["Shuhei Ohno"] -version = "1.0.0-DEV" +version = "0.0.16" [deps] -Revise = "295af30f-e4ad-537b-8983-00126c2a3abe" SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b" -Weave = "44d3d7a6-8a23-5bf8-98c5-b353f8df5ec9" + +[weakdeps] +Revise = "295af30f-e4ad-537b-8983-00126c2a3abe" [compat] julia = "1.1" [extras] +LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f" +Latexify = "23fbe1c1-3f47-55db-b15f-69d7ec21a316" +Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a" +Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7" +QuadGK = "1fd47b50-473d-5c70-9696-f719f8f3bcdc" +Suppressor = "fd094767-a336-5f1f-9728-57cf17d0bbfb" +Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7" Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" [targets] -test = ["Test"] +test = ["Test", "Suppressor", "Printf", "Markdown", "QuadGK", "Symbolics", "Latexify", "LaTeXStrings"] diff --git a/README.md b/README.md index 9c2e772..f91c0fd 100644 --- a/README.md +++ b/README.md @@ -1,8 +1,7 @@ # Antiq.jl +[![Build Status](https://github.com/ohno/Antiq.jl/actions/workflows/CI.yml/badge.svg?branch=main)](https://github.com/ohno/Antiq.jl/actions/workflows/CI.yml?query=branch%3Amain) [![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://ohno.github.io/Antiq.jl/stable/) [![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://ohno.github.io/Antiq.jl/dev/) -[![Build Status](https://github.com/ohno/Antiq.jl/actions/workflows/CI.yml/badge.svg?branch=main)](https://github.com/ohno/Antiq.jl/actions/workflows/CI.yml?query=branch%3Amain) -[![Coverage](https://codecov.io/gh/ohno/Antiq.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/ohno/Antiq.jl) Please see [here](https://ohno.github.io/Antiq.jl/dev/HydrogenAtom/). \ No newline at end of file diff --git a/developer.ipynb b/developer.ipynb index cb5e090..151741d 100644 --- a/developer.ipynb +++ b/developer.ipynb @@ -13,9 +13,7 @@ "source": [ "## PkgTemplates.jl\n", "\n", - "~~https://qiita.com/cometscome_phys/items/989389db3540ebd9e026#%E3%83%AA%E3%83%AA%E3%83%BC%E3%82%B9%E3%81%AE%E7%99%BB%E9%8C%B2~~\n", - "\n", - "https://juliaci.github.io/PkgTemplates.jl/stable/user/#A-More-Complicated-Example-1\n", + "https://qiita.com/SatoshiTerasaki/items/7dbb809c962e794a9df6\n", "\n", "```julia\n", "# using Pkg\n", @@ -24,20 +22,28 @@ "\n", "t = Template(;\n", " user=\"ohno\",\n", - " authors=[\"Shuhei Ohno\"],\n", - " dir=\"../\",\n", - " julia=v\"1.1\",\n", - " plugins=[\n", - " License(; name=\"MIT\"),\n", - " Git(; manifest=true, ssh=true),\n", - " GitHubActions(; x86=true),\n", - " Codecov(),\n", + " authors = [\"Shuhei Ohno\"]\n", + " dir = pwd(),\n", + " julia=v\"1\",\n", + " plugins = [\n", + " License(; name = \"MIT\"),\n", + " ProjectFile(; version=v\"0.0.1\"),\n", + " Git(; manifest = false, ssh = true),\n", + " GitHubActions(;\n", + " extra_versions = [\"1.6\", \"1.7\", \"nightly\"]\n", + " ),\n", " Documenter{GitHubActions}(),\n", + " Readme(;\n", + " inline_badges = true,\n", + " badge_order = DataType[\n", + " GitHubActions,\n", + " Documenter{GitHubActions},\n", + " ],\n", + " ),\n", " ],\n", ")\n", "\n", "generate(\"Antiq.jl\", t)\n", - "mv(\"Antiq\", \"Antiq.jl\")\n", "```" ] }, @@ -76,22 +82,23 @@ "name": "stderr", "output_type": "stream", "text": [ - "\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m project at `C:\\Users\\user\\Desktop\\GitHub\\Antiq.jl`\n" + "\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m project at `C:\\Users\\user\\Desktop\\GitHub\\Antiq.jl`\n", + "\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `C:\\Users\\user\\Desktop\\GitHub\\Antiq.jl\\Project.toml`\n", + "\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `C:\\Users\\user\\Desktop\\GitHub\\Antiq.jl\\Manifest.toml`\n" ] } ], "source": [ "versioninfo()\n", + "\n", "using Pkg\n", + "# Pkg.add(\"Weave\")\n", "# Pkg.add(\"Revise\")\n", + "# using Weave\n", "using Revise\n", - "Pkg.activate(\"./\")\n", - "\n", - "# # Dependency\n", - "# Pkg.add(\"SpecialFunctions\")\n", - "# using SpecialFunctions\n", "\n", - "# Antiq.jl\n", + "Pkg.activate(\"./\")\n", + "Pkg.resolve()\n", "using Antiq" ] }, @@ -218,7 +225,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Weave.jl" + "## runtests" ] }, { @@ -232,25 +239,208 @@ "name": "stderr", "output_type": "stream", "text": [ + "\u001b[32m\u001b[1m Testing\u001b[22m\u001b[39m Antiq\n", + "\u001b[32m\u001b[1m Status\u001b[22m\u001b[39m `C:\\Users\\user\\AppData\\Local\\Temp\\jl_Qj7MVW\\Project.toml`\n", + " \u001b[90m [be6e5d0e] \u001b[39mAntiq v0.0.16 `C:\\Users\\user\\Desktop\\GitHub\\Antiq.jl`\n", + " \u001b[90m [b964fa9f] \u001b[39mLaTeXStrings v1.3.1\n", + " \u001b[90m [23fbe1c1] \u001b[39mLatexify v0.16.1\n", + " \u001b[90m [1fd47b50] \u001b[39mQuadGK v2.9.1\n", + "\u001b[32m⌃\u001b[39m\u001b[90m [276daf66] \u001b[39mSpecialFunctions v2.3.0\n", + " \u001b[90m [fd094767] \u001b[39mSuppressor v0.2.6\n", + " \u001b[90m [0c5d862f] \u001b[39mSymbolics v5.10.0\n", + " \u001b[90m [d6f4376e] \u001b[39mMarkdown `@stdlib/Markdown`\n", + " \u001b[90m [de0858da] \u001b[39mPrintf `@stdlib/Printf`\n", + " \u001b[90m [8dfed614] \u001b[39mTest `@stdlib/Test`\n", + "\u001b[32m\u001b[1m Status\u001b[22m\u001b[39m `C:\\Users\\user\\AppData\\Local\\Temp\\jl_Qj7MVW\\Manifest.toml`\n", + " 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\u001b[39mOpenSpecFun_jll v0.5.5+0\n", + " \u001b[90m [f50d1b31] \u001b[39mRmath_jll v0.4.0+0\n", + " \u001b[90m [0dad84c5] \u001b[39mArgTools v1.1.1 `@stdlib/ArgTools`\n", + " \u001b[90m [56f22d72] \u001b[39mArtifacts `@stdlib/Artifacts`\n", + " \u001b[90m [2a0f44e3] \u001b[39mBase64 `@stdlib/Base64`\n", + " \u001b[90m [ade2ca70] \u001b[39mDates `@stdlib/Dates`\n", + " \u001b[90m [8ba89e20] \u001b[39mDistributed `@stdlib/Distributed`\n", + " \u001b[90m [f43a241f] \u001b[39mDownloads v1.6.0 `@stdlib/Downloads`\n", + " \u001b[90m [7b1f6079] \u001b[39mFileWatching `@stdlib/FileWatching`\n", + " \u001b[90m [9fa8497b] \u001b[39mFuture `@stdlib/Future`\n", + " \u001b[90m [b77e0a4c] \u001b[39mInteractiveUtils `@stdlib/InteractiveUtils`\n", + " \u001b[90m [b27032c2] \u001b[39mLibCURL v0.6.3 `@stdlib/LibCURL`\n", + " \u001b[90m [76f85450] \u001b[39mLibGit2 `@stdlib/LibGit2`\n", + " \u001b[90m [8f399da3] \u001b[39mLibdl `@stdlib/Libdl`\n", + " \u001b[90m [37e2e46d] \u001b[39mLinearAlgebra 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+ " \u001b[90m [a4e569a6] \u001b[39mTar v1.10.1 `@stdlib/Tar`\n", + " \u001b[90m [8dfed614] \u001b[39mTest `@stdlib/Test`\n", + " \u001b[90m [cf7118a7] \u001b[39mUUIDs `@stdlib/UUIDs`\n", + " \u001b[90m [4ec0a83e] \u001b[39mUnicode `@stdlib/Unicode`\n", + " \u001b[90m [e66e0078] \u001b[39mCompilerSupportLibraries_jll v0.5.2+0 `@stdlib/CompilerSupportLibraries_jll`\n", + " \u001b[90m [deac9b47] \u001b[39mLibCURL_jll v7.84.0+0 `@stdlib/LibCURL_jll`\n", + " \u001b[90m [29816b5a] \u001b[39mLibSSH2_jll v1.10.2+0 `@stdlib/LibSSH2_jll`\n", + " \u001b[90m [c8ffd9c3] \u001b[39mMbedTLS_jll v2.28.0+0 `@stdlib/MbedTLS_jll`\n", + " \u001b[90m [14a3606d] \u001b[39mMozillaCACerts_jll v2022.2.1 `@stdlib/MozillaCACerts_jll`\n", + " \u001b[90m [4536629a] \u001b[39mOpenBLAS_jll v0.3.20+0 `@stdlib/OpenBLAS_jll`\n", + " \u001b[90m [05823500] \u001b[39mOpenLibm_jll v0.8.1+0 `@stdlib/OpenLibm_jll`\n", + " \u001b[90m [83775a58] \u001b[39mZlib_jll v1.2.12+3 `@stdlib/Zlib_jll`\n", + " \u001b[90m [8e850b90] \u001b[39mlibblastrampoline_jll v5.1.1+0 `@stdlib/libblastrampoline_jll`\n", + " \u001b[90m [8e850ede] \u001b[39mnghttp2_jll v1.48.0+0 `@stdlib/nghttp2_jll`\n", + " \u001b[90m [3f19e933] \u001b[39mp7zip_jll v17.4.0+0 `@stdlib/p7zip_jll`\n", + "\u001b[36m\u001b[1m Info\u001b[22m\u001b[39m Packages marked with \u001b[32m⌃\u001b[39m and \u001b[33m⌅\u001b[39m have new versions available, but those with \u001b[33m⌅\u001b[39m are restricted by compatibility constraints from upgrading.\n", + "\u001b[32m\u001b[1m Testing\u001b[22m\u001b[39m Running tests...\n", + "WARNING: replacing module MorsePotential1669411154543485985.\n", + "\u001b[0m\u001b[1mTest Summary: | \u001b[22m\u001b[32m\u001b[1mPass \u001b[22m\u001b[39m\u001b[36m\u001b[1mTotal \u001b[22m\u001b[39m\u001b[0m\u001b[1m Time\u001b[22m\n", + "Antiq.jl | \u001b[32m2052 \u001b[39m\u001b[36m 2052 \u001b[39m\u001b[0m1m33.8s\n", + "\u001b[32m\u001b[1m Testing\u001b[22m\u001b[39m Antiq tests passed \n" + ] + } + ], + "source": [ + "# pwd() |> display\n", + "# include(\"./test/runtests.jl\")\n", + "Pkg.test()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Weave.jl" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "The latest version of Julia in the `release` channel is 1.9.4+0.x64.w64.mingw32. You currently have `1.9.2+0.x64.w64.mingw32` installed. Run:\n", + "\n", + " juliaup update\n", + "\n", + "to install Julia 1.9.4+0.x64.w64.mingw32 and update the `release` channel to that version.\n", "┌ Info: Weaving chunk 1 from line 55\n", - "│ progress = 0.0\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.0\n", "┌ Info: Weaving chunk 2 from line 62\n", - "│ progress = 0.16666666666666666\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.16666666666666666\n", "┌ Info: Weaving chunk 3 from line 70\n", - "│ progress = 0.3333333333333333\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.3333333333333333\n", "┌ Info: Weaving chunk 4 from line 77\n", - "│ progress = 0.5\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.5\n", "┌ Info: Weaving chunk 5 from line 89\n", - "│ progress = 0.6666666666666666\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.6666666666666666\n", "┌ Info: Weaving chunk 6 from line 107\n", - "│ progress = 0.8333333333333334\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", - "WARNING: replacing module InfinitePotentialWell8472295553246349096.\n" + "└ progress = 0.8333333333333334\n", + "WARNING: replacing module InfinitePotentialWell8472295553246349096.\n", + "┌ Info: Weaved all chunks\n", + "└ progress = 1\n" ] }, { @@ -258,7 +448,21 @@ "output_type": "stream", "text": [ "m.match = \".jl\\\")\\n```\\n\\n```\"\n", - "m.offset = 3032\n", + "m.offset = " + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "[ Info: Weaved to C:\\Users\\user\\Desktop\\GitHub\\Antiq.jl\\docs\\src\\InfinitePotentialWell.md\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3032\n", "m.match = \"```\\n```\\n\\n\\n\"\n", "m.offset = 25354\n" ] @@ -267,38 +471,23 @@ "name": "stderr", "output_type": "stream", "text": [ - "┌ Info: Weaved all chunks\n", - "│ progress = 1\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:90\n", - "┌ Info: Weaved to C:\\Users\\user\\Desktop\\GitHub\\Antiq.jl\\docs\\src\\InfinitePotentialWell.md\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\Weave.jl:228\n", "┌ Info: Weaving chunk 1 from line 93\n", - "│ progress = 0.0\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.0\n", "┌ Info: Weaving chunk 2 from line 100\n", - "│ progress = 0.14285714285714285\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.14285714285714285\n", "┌ Info: Weaving chunk 3 from line 108\n", - "│ progress = 0.2857142857142857\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.2857142857142857\n", "┌ Info: Weaving chunk 4 from line 115\n", - "│ progress = 0.42857142857142855\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.42857142857142855\n", "┌ Info: Weaving chunk 5 from line 122\n", - "│ progress = 0.5714285714285714\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.5714285714285714\n", "┌ Info: Weaving chunk 6 from line 134\n", - "│ progress = 0.7142857142857143\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.7142857142857143\n", "┌ Info: Weaving chunk 7 from line 152\n", - "│ progress = 0.8571428571428571\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.8571428571428571\n", "WARNING: replacing module HarmonicOscillator3094684212771689889.\n", "┌ Info: Weaved all chunks\n", - "│ progress = 1\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:90\n", - "┌ Info: Weaved to C:\\Users\\user\\Desktop\\GitHub\\Antiq.jl\\docs\\src\\HarmonicOscillator.md\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\Weave.jl:228\n" + "└ progress = 1\n" ] }, { @@ -308,36 +497,32 @@ "m.match = \".jl\\\")\\n```\\n\\n```\"\n", "m.offset = 6290\n", "m.match = \"```\\n```\\n\\n\\n\"\n", - "m.offset = 31655\n" + "m.offset = 32717\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ + "[ Info: Weaved to C:\\Users\\user\\Desktop\\GitHub\\Antiq.jl\\docs\\src\\HarmonicOscillator.md\n", "┌ Info: Weaving chunk 1 from line 85\n", - "│ progress = 0.0\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.0\n", "┌ Info: Weaving chunk 2 from line 92\n", - "│ progress = 0.14285714285714285\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.14285714285714285\n", "┌ Info: Weaving chunk 3 from line 102\n", - "│ progress = 0.2857142857142857\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.2857142857142857\n", "┌ Info: Weaving chunk 4 from line 109\n", - "│ progress = 0.42857142857142855\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.42857142857142855\n", "┌ Info: Weaving chunk 5 from line 116\n", - "│ progress = 0.5714285714285714\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.5714285714285714\n", "┌ Info: Weaving chunk 6 from line 129\n", - "│ progress = 0.7142857142857143\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.7142857142857143\n", "WARNING: replacing module MorsePotential1669411154543485985.\n", "┌ Info: Weaving chunk 7 from line 152\n", - "│ progress = 0.8571428571428571\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", - "WARNING: replacing module MorsePotential1669411154543485985.\n" + "└ progress = 0.8571428571428571\n", + "WARNING: replacing module MorsePotential1669411154543485985.\n", + "┌ Info: Weaved all chunks\n", + "└ progress = 1\n" ] }, { @@ -347,46 +532,32 @@ "m.match = \".jl\\\")\\n```\\n\\n```\"\n", "m.offset = 5890\n", "m.match = \"```\\n```\\n\\n\\n\"\n", - "m.offset = 52840\n" + "m.offset = 53552\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "┌ Info: Weaved all chunks\n", - "│ progress = 1\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:90\n", - "┌ Info: Weaved to C:\\Users\\user\\Desktop\\GitHub\\Antiq.jl\\docs\\src\\MorsePotential.md\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\Weave.jl:228\n", + "[ Info: Weaved to C:\\Users\\user\\Desktop\\GitHub\\Antiq.jl\\docs\\src\\MorsePotential.md\n", "┌ Info: Weaving chunk 1 from line 156\n", - "│ progress = 0.0\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", - "WARNING: replacing module HydrogenAtom11641542298082958385.\n", + "└ progress = 0.0\n", "┌ Info: Weaving chunk 2 from line 163\n", - "│ progress = 0.1111111111111111\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.1111111111111111\n", "┌ Info: Weaving chunk 3 from line 173\n", - "│ progress = 0.2222222222222222\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.2222222222222222\n", "┌ Info: Weaving chunk 4 from line 180\n", - "│ progress = 0.3333333333333333\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.3333333333333333\n", "┌ Info: Weaving chunk 5 from line 188\n", - "│ progress = 0.4444444444444444\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.4444444444444444\n", "┌ Info: Weaving chunk 6 from line 213\n", - "│ progress = 0.5555555555555556\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.5555555555555556\n", "┌ Info: Weaving chunk 7 from line 221\n", - "│ progress = 0.6666666666666666\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.6666666666666666\n", "┌ Info: Weaving chunk 8 from line 232\n", - "│ progress = 0.7777777777777778\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.7777777777777778\n", "┌ Info: Weaving chunk 9 from line 247\n", - "│ progress = 0.8888888888888888\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:66\n", + "└ progress = 0.8888888888888888\n", "WARNING: replacing module HydrogenAtom11641542298082958385.\n", "WARNING: replacing module MorsePotential1669411154543485985.\n" ] @@ -398,7 +569,7 @@ "m.match = \".jl\\\")\\n```\\n\\n```\"\n", "m.offset = 13690\n", "m.match = \"```\\n```\\n\\n\\n\"\n", - "m.offset = 102783\n" + "m.offset = 104725\n" ] }, { @@ -406,41 +577,23 @@ "output_type": "stream", "text": [ "┌ Info: Weaved all chunks\n", - "│ progress = 1\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\run.jl:90\n", - "┌ Info: Weaved to C:\\Users\\user\\Desktop\\GitHub\\Antiq.jl\\docs\\src\\HydrogenAtom.md\n", - "└ @ Weave C:\\Users\\user\\.julia\\packages\\Weave\\f7Ly3\\src\\Weave.jl:228\n" + "└ progress = 1\n", + "[ Info: Weaved to C:\\Users\\user\\Desktop\\GitHub\\Antiq.jl\\docs\\src\\HydrogenAtom.md\n" ] + }, + { + "data": { + "text/plain": [ + "Process(`\u001b[4mjulia\u001b[24m \u001b[4m--project=docs/\u001b[24m \u001b[4m-e\u001b[24m \u001b[4m'cd(\"docs\"); include(\"jmd2md.jl\")'\u001b[24m`, ProcessExited(0))" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "# import Pkg; Pkg.add(\"Weave\")\n", - "using Weave\n", - "\n", - "files = [\n", - " \"InfinitePotentialWell\"\n", - " \"HarmonicOscillator\"\n", - " \"MorsePotential\"\n", - " \"HydrogenAtom\"\n", - "]\n", - "\n", - "for file in files\n", - " weave(\"./docs/src/jmd/$file.jmd\", doctype=\"github\", out_path=\"./docs/src/\", fig_path=\"./assets/fig/\")\n", - " text = Antiq.load(\"./docs/src/$file.md\")\n", - " # remove ``` after include(...s)\n", - " for m in eachmatch(r\"\\.jl\\\"\\)\\n```[.\\n]*?```\", text)\n", - " @show m.match\n", - " @show m.offset\n", - " text = replace(text, m.match => \".jl\\\")\\n```\")\n", - " end\n", - " # remove ``` at the end of file\n", - " for m in eachmatch(r\"```\\n```[\\s\\n]*?\\z\", text)\n", - " @show m.match\n", - " @show m.offset\n", - " text = replace(text, m.match => \"\\n```\\n\")\n", - " end\n", - " Antiq.save(\"./docs/src/$file.md\", text)\n", - "end" + "run(`julia --project=docs/ -e 'cd(\"docs\"); include(\"jmd2md.jl\")'`)" ] }, { @@ -452,76 +605,34 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "┌ Info: SetupBuildDirectory: setting up build directory.\n", - "└ @ Documenter.Builder C:\\Users\\user\\.julia\\packages\\Documenter\\H5y27\\src\\Builder.jl:87\n", - "┌ Info: Doctest: running doctests.\n", - "└ @ Documenter.Builder C:\\Users\\user\\.julia\\packages\\Documenter\\H5y27\\src\\Builder.jl:212\n", - "┌ Info: ExpandTemplates: expanding markdown templates.\n", - "└ @ Documenter.Builder C:\\Users\\user\\.julia\\packages\\Documenter\\H5y27\\src\\Builder.jl:225\n", - "┌ Info: CrossReferences: building cross-references.\n", - "└ @ Documenter.Builder C:\\Users\\user\\.julia\\packages\\Documenter\\H5y27\\src\\Builder.jl:231\n", - "┌ Info: CheckDocument: running document checks.\n", - "└ @ Documenter.Builder C:\\Users\\user\\.julia\\packages\\Documenter\\H5y27\\src\\Builder.jl:237\n", - "┌ Info: Populate: populating indices.\n", - "└ @ Documenter.Builder C:\\Users\\user\\.julia\\packages\\Documenter\\H5y27\\src\\Builder.jl:245\n", - "┌ Info: RenderDocument: rendering document.\n", - "└ @ Documenter.Builder C:\\Users\\user\\.julia\\packages\\Documenter\\H5y27\\src\\Builder.jl:260\n", - "┌ Info: HTMLWriter: rendering HTML pages.\n", - "└ @ Documenter.Writers.HTMLWriter C:\\Users\\user\\.julia\\packages\\Documenter\\H5y27\\src\\Writers\\HTMLWriter.jl:714\n", + "The latest version of Julia in the `release` channel is 1.9.4+0.x64.w64.mingw32. You currently have `1.9.2+0.x64.w64.mingw32` installed. Run:\n", + "\n", + " juliaup update\n", + "\n", + "to install Julia 1.9.4+0.x64.w64.mingw32 and update the `release` channel to that version.\n", + "[ Info: SetupBuildDirectory: setting up build directory.\n", + "[ Info: Doctest: running doctests.\n", + "[ Info: ExpandTemplates: expanding markdown templates.\n", + "[ Info: CrossReferences: building cross-references.\n", + "[ Info: CheckDocument: running document checks.\n", + "[ Info: Populate: populating indices.\n", + "[ Info: RenderDocument: rendering document.\n", + "[ Info: HTMLWriter: rendering HTML pages.\n", "┌ Warning: Documenter could not auto-detect the building environment Skipping deployment.\n", - "└ @ Documenter C:\\Users\\user\\.julia\\packages\\Documenter\\H5y27\\src\\deployconfig.jl:75\n" - ] - } - ], - "source": [ - "# run(`cmd /C cd \\& julia ./docs/make.jl`)\n", - "include(\"./docs/make.jl\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## runtests" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "WARNING: replacing module InfinitePotentialWell8472295553246349096.\n", - "WARNING: replacing module HarmonicOscillator3094684212771689889.\n", - "WARNING: replacing module MorsePotential1669411154543485985.\n", - "WARNING: replacing module HydrogenAtom11641542298082958385.\n", - "WARNING: replacing module MorsePotential1669411154543485985.\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\u001b[0m\u001b[1mTest Summary: | \u001b[22m\u001b[32m\u001b[1mPass \u001b[22m\u001b[39m\u001b[36m\u001b[1mTotal \u001b[22m\u001b[39m\u001b[0m\u001b[1m Time\u001b[22m\n", - "Antiq.jl | \u001b[32m2052 \u001b[39m\u001b[36m 2052 \u001b[39m\u001b[0m44.4s\n" + "└ @ Documenter C:\\Users\\user\\.julia\\packages\\Documenter\\bYYzK\\src\\deployconfig.jl:75\n" ] }, { "data": { "text/plain": [ - "Test.DefaultTestSet(\"Antiq.jl\", Any[Test.DefaultTestSet(\"<ψᵢ|ψⱼ> = ∫ψₙ*ψₙdx = δᵢⱼ\", Any[], 100, false, false, true, 1.701193274726e9, 1.701193275384e9), Test.DefaultTestSet(\"<ψₙ|H|ψₙ> = ∫ψₙ*Tψₙdx = Eₙ\", Any[], 80, false, false, true, 1.701193275393e9, 1.701193276053e9), Test.DefaultTestSet(\"<ψₙ|x|ψₙ> = L/2\", Any[], 4, false, false, true, 1.701193276059e9, 1.701193276423e9), Test.DefaultTestSet(\"<ψₙ|x²|ψₙ> = 2L²/π³(π³/6-π/4)\", Any[], 4, false, false, true, 1.701193276433e9, 1.701193276847e9), Test.DefaultTestSet(\"<ψₙ|p|ψₙ> = ∫ψₙ*(-iℏd/dx)ψₙdx = 0\", Any[], 4, false, false, true, 1.701193276857e9, 1.701193277383e9), Test.DefaultTestSet(\"<ψₙ|p²|ψₙ> = ∫ψₙ*(-ℏ²d²/dx²)ψₙdx = π²ℏ²/L²\", Any[], 4, false, false, true, 1.701193277403e9, 1.701193277881e9), Test.DefaultTestSet(\"Hₙ(x) = (-1)ⁿ exp(x²) dⁿ/dxⁿ　exp(-x²) = ...\", Any[], 10, false, false, true, 1.701193277918e9, 1.701193278115e9), Test.DefaultTestSet(\"∫Hⱼ(x)Hᵢ(x)exp(-x²)dx = √π2ʲj!δᵢⱼ\", Any[], 100, false, false, true, 1.701193278124e9, 1.7011932788e9), Test.DefaultTestSet(\"<ψᵢ|ψⱼ> = δᵢⱼ\", Any[], 100, false, false, true, 1.70119327881e9, 1.701193279526e9), Test.DefaultTestSet(\"2 × <ψₙ|V|ψₙ> = Eₙ\", Any[], 40, false, false, true, 1.701193279531e9, 1.701193280049e9) … Test.DefaultTestSet(\"Pₙᵐ(x) = √(1-x²)ᵐ dᵐ/dxᵐ Pₙ(x); Pₙ(x) = 1/(2ⁿn!) dⁿ/dxⁿ (x²-1)ⁿ\", Any[], 15, false, false, true, 1.701193286143e9, 1.701193286309e9), Test.DefaultTestSet(\"∫Pᵢᵐ(x)Pⱼᵐ(x)dx = 2(j+m)!/(2j+1)(j-m)! δᵢⱼ\", Any[], 355, false, false, true, 1.701193286321e9, 1.701193287009e9), Test.DefaultTestSet(\"∫Yₗ₁ₘ₁(θ,φ)Yₗ₂ₘ₂(θ,φ)sinθdθdφ = δₗ₁ₗ₂δₘ₁ₘ₂\", Any[], 81, false, false, true, 1.70119328702e9, 1.701193288943e9), Test.DefaultTestSet(\"Lₙᵏ(x) = dᵏ/dxᵏ Lₙ(x); Lₙ(x) = 1/(n!) eˣ dⁿ/dxⁿ e⁻ˣ xⁿ\", Any[], 15, false, false, true, 1.70119328895e9, 1.701193289218e9), Test.DefaultTestSet(\"∫exp(-x)xᵏLᵢᵏ(x)Lⱼᵏ(x)dx = (2i+k)!/(i+k)! δᵢⱼ\", Any[], 204, false, false, true, 1.701193289228e9, 1.701193289921e9), Test.DefaultTestSet(\"∫|Rₙₗ(r)|²r²dr = δₙ₁ₙ₂δₗ₁ₗ₂\", Any[], 45, false, false, true, 1.70119328993e9, 1.701193290451e9), Test.DefaultTestSet(\"∫r|Rₙₗ(r)|²r²dr = (a₀×mₑ/μ)/2Z × [3n²-l(l+1)]; 1/μ = 1/mₑ + 1/mₚ\", Any[], 45, false, false, true, 1.701193290456e9, 1.70119329088e9), Test.DefaultTestSet(\"∫r²|Rₙₗ(r)|²r²dr = (a₀×mₑ/μ)²/2Z² × n²[5n²+1-3l(l+1)]; 1/μ = 1/mₑ + 1/mₚ\", Any[], 45, false, false, true, 1.701193290887e9, 1.701193291336e9), Test.DefaultTestSet(\"<ψₙ|V|ψₙ> / 2 = Eₙ\", Any[], 10, false, false, true, 1.70119329134e9, 1.701193291834e9), Test.DefaultTestSet(\"<ψₙ₁ₗ₁ₘ₁|ψₙ₂ₗ₂ₘ₂> = δₙ₁ₙ₂δₗ₁ₗ₂δₘ₁ₘ₂\", Any[], 196, false, false, true, 1.701193291842e9, 1.701193318941e9)], 0, false, false, true, 1.701193274569e9, 1.701193318941e9)" + "Process(`\u001b[4mjulia\u001b[24m \u001b[4m--project=docs/\u001b[24m \u001b[4m-e\u001b[24m \u001b[4m'cd(\"docs\"); include(\"make.jl\")'\u001b[24m`, ProcessExited(0))" ] }, "execution_count": 5, @@ -530,8 +641,9 @@ } ], "source": [ - "# pwd() |> display\n", - "include(\"./test/runtests.jl\")" + "# run(`cmd /C cd \\& julia ./docs/make.jl`)\n", + "# include(\"./docs/make.jl\")\n", + "run(`julia --project=docs/ -e 'cd(\"docs\"); include(\"make.jl\")'`)" ] } ], diff --git a/docs/Project.toml b/docs/Project.toml index 3a3e3b5..c5c56a2 100644 --- a/docs/Project.toml +++ b/docs/Project.toml @@ -1,3 +1,4 @@ [deps] Antiq = "be6e5d0e-34a5-4c8f-af83-e1b5389203d8" +Weave = "44d3d7a6-8a23-5bf8-98c5-b353f8df5ec9" Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" diff --git a/docs/jmd2md.jl b/docs/jmd2md.jl new file mode 100644 index 0000000..b004d2c --- /dev/null +++ b/docs/jmd2md.jl @@ -0,0 +1,20 @@ +using Antiq +using Weave + +for file in Antiq.models + weave("./src/jmd/$file.jmd", doctype="github", out_path="./src/", fig_path="./assets/fig/") + text = Antiq.load("./src/$file.md") + # remove ``` after include(...s) + for m in eachmatch(r"\.jl\"\)\n```[.\n]*?```", text) + @show m.match + @show m.offset + text = replace(text, m.match => ".jl\")\n```") + end + # remove ``` at the end of file + for m in eachmatch(r"```\n```[\s\n]*?\z", text) + @show m.match + @show m.offset + text = replace(text, m.match => "\n```\n") + end + Antiq.save("./src/$file.md", text) +end diff --git a/docs/src/HarmonicOscillator.md b/docs/src/HarmonicOscillator.md index fdabfb6..c77f31a 100644 --- a/docs/src/HarmonicOscillator.md +++ b/docs/src/HarmonicOscillator.md @@ -193,7 +193,7 @@ include("../../../test/HarmonicOscillator.jl") ```math \begin{aligned} H_{0}(x) - = e^{x^{2}} e^{ - x^{2}} + = e^{ - x^{2}} e^{x^{2}} &= 1 \\ &= 1 \end{aligned} @@ -213,7 +213,7 @@ include("../../../test/HarmonicOscillator.jl") ```math \begin{aligned} H_{2}(x) - = e^{x^{2}} \frac{\mathrm{d}^{2} e^{ - x^{2}}}{\mathrm{d}x^{2}} + = e^{x^{2}} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d} e^{ - x^{2}}}{\mathrm{d}x} &= -2 + 4 x^{2} \\ &= -2 + 4 x^{2} \end{aligned} @@ -223,9 +223,9 @@ include("../../../test/HarmonicOscillator.jl") ```math \begin{aligned} H_{3}(x) - = - e^{x^{2}} \frac{\mathrm{d}^{3} e^{ - x^{2}}}{\mathrm{d}x^{3}} - &= 8 x^{3} - 12 x \\ - &= 8 x^{3} - 12 x + = - \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d} e^{ - x^{2}}}{\mathrm{d}x} e^{x^{2}} + &= - 12 x + 8 x^{3} \\ + &= - 12 x + 8 x^{3} \end{aligned} ``` @@ -233,7 +233,7 @@ include("../../../test/HarmonicOscillator.jl") ```math \begin{aligned} H_{4}(x) - = e^{x^{2}} \frac{\mathrm{d}^{4} e^{ - x^{2}}}{\mathrm{d}x^{4}} + = e^{x^{2}} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d} e^{ - x^{2}}}{\mathrm{d}x} &= 12 - 48 x^{2} + 16 x^{4} \\ &= 12 - 48 x^{2} + 16 x^{4} \end{aligned} @@ -243,9 +243,9 @@ include("../../../test/HarmonicOscillator.jl") ```math \begin{aligned} H_{5}(x) - = - e^{x^{2}} \frac{\mathrm{d}^{5} e^{ - x^{2}}}{\mathrm{d}x^{5}} - &= 32 x^{5} + 120 x - 160 x^{3} \\ - &= 32 x^{5} + 120 x - 160 x^{3} + = - \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d} e^{ - x^{2}}}{\mathrm{d}x} e^{x^{2}} + &= 120 x - 160 x^{3} + 32 x^{5} \\ + &= 120 x - 160 x^{3} + 32 x^{5} \end{aligned} ``` @@ -253,9 +253,9 @@ include("../../../test/HarmonicOscillator.jl") ```math \begin{aligned} H_{6}(x) - = e^{x^{2}} \frac{\mathrm{d}^{6} e^{ - x^{2}}}{\mathrm{d}x^{6}} - &= -120 + 720 x^{2} + 64 x^{6} - 480 x^{4} \\ - &= -120 + 720 x^{2} + 64 x^{6} - 480 x^{4} + = e^{x^{2}} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d} e^{ - x^{2}}}{\mathrm{d}x} + &= -120 + 720 x^{2} - 480 x^{4} + 64 x^{6} \\ + &= -120 + 720 x^{2} - 480 x^{4} + 64 x^{6} \end{aligned} ``` @@ -263,9 +263,9 @@ include("../../../test/HarmonicOscillator.jl") ```math \begin{aligned} H_{7}(x) - = - e^{x^{2}} \frac{\mathrm{d}^{7} e^{ - x^{2}}}{\mathrm{d}x^{7}} - &= 128 x^{7} - 1344 x^{5} - 1680 x + 3360 x^{3} \\ - &= 128 x^{7} - 1344 x^{5} - 1680 x + 3360 x^{3} + = - e^{x^{2}} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d} e^{ - x^{2}}}{\mathrm{d}x} + &= - 1680 x + 3360 x^{3} - 1344 x^{5} + 128 x^{7} \\ + &= - 1680 x + 3360 x^{3} - 1344 x^{5} + 128 x^{7} \end{aligned} ``` @@ -273,9 +273,9 @@ include("../../../test/HarmonicOscillator.jl") ```math \begin{aligned} H_{8}(x) - = e^{x^{2}} \frac{\mathrm{d}^{8} e^{ - x^{2}}}{\mathrm{d}x^{8}} - &= 1680 - 13440 x^{2} - 3584 x^{6} + 13440 x^{4} + 256 x^{8} \\ - &= 1680 - 13440 x^{2} - 3584 x^{6} + 13440 x^{4} + 256 x^{8} + = e^{x^{2}} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d} e^{ - x^{2}}}{\mathrm{d}x} + &= 1680 - 13440 x^{2} + 13440 x^{4} - 3584 x^{6} + 256 x^{8} \\ + &= 1680 - 13440 x^{2} + 13440 x^{4} - 3584 x^{6} + 256 x^{8} \end{aligned} ``` @@ -283,15 +283,15 @@ include("../../../test/HarmonicOscillator.jl") ```math \begin{aligned} H_{9}(x) - = - e^{x^{2}} \frac{\mathrm{d}^{9} e^{ - x^{2}}}{\mathrm{d}x^{9}} - &= 512 x^{9} - 9216 x^{7} + 30240 x + 48384 x^{5} - 80640 x^{3} \\ - &= 512 x^{9} - 9216 x^{7} + 30240 x + 48384 x^{5} - 80640 x^{3} + = - e^{x^{2}} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d} e^{ - x^{2}}}{\mathrm{d}x} + &= 30240 x - 80640 x^{3} + 48384 x^{5} - 9216 x^{7} + 512 x^{9} \\ + &= 30240 x - 80640 x^{3} + 48384 x^{5} - 9216 x^{7} + 512 x^{9} \end{aligned} ``` ``` Test Summary: | Pass Total Time -Hₙ(x) = (-1)ⁿ exp(x²) dⁿ/dxⁿ　exp(-x²) = ... | 10 10 34.9s +Hₙ(x) = (-1)ⁿ exp(x²) dⁿ/dxⁿ exp(-x²) = ... | 10 10 35.0s ``` #### Normalization & Orthogonality of $H_n(x)$ @@ -403,7 +403,7 @@ Hₙ(x) = (-1)ⁿ exp(x²) dⁿ/dxⁿ　exp(-x²) = ... | 10 10 34.9s 9 8 0.0000000016298145 0.0000000000000000 0.0000000000000000% ✔ 9 9 329312283.3492956757545471 329312283.3492959141731262 0.0000000000000724% ✔ Test Summary: | Pass Total Time -∫Hⱼ(x)Hᵢ(x)exp(-x²)dx = √π2ʲj!δᵢⱼ | 100 100 1.0s +∫Hⱼ(x)Hᵢ(x)exp(-x²)dx = √π2ʲj!δᵢⱼ | 100 100 1.2s ``` #### Normalization & Orthogonality of $\psi_n(x)$ @@ -515,7 +515,7 @@ Test Summary: | Pass Total Time 9 8 -0.0000000000000000 0.0000000000000000 0.0000000000000000% ✔ 9 9 0.9999999999999998 1.0000000000000000 0.0000000000000222% ✔ Test Summary: | Pass Total Time -<ψᵢ|ψⱼ> = δᵢⱼ | 100 100 0.7s +<ψᵢ|ψⱼ> = δᵢⱼ | 100 100 1.2s ``` #### Virial Theorem @@ -569,7 +569,7 @@ The virial theorem $\langle T \rangle = \langle V \rangle$ and the definition of 5.0 8 8.4999999999999929 8.5000000000000000 0.0000000000000836% ✔ 5.0 9 9.5000000000000000 9.5000000000000000 0.0000000000000000% ✔ Test Summary: | Pass Total Time -2 × <ψₙ|V|ψₙ> = Eₙ | 40 40 0.6s +2 × <ψₙ|V|ψₙ> = Eₙ | 40 40 1.0s ``` #### Eigen Values @@ -677,6 +677,6 @@ are given by the sum of 2 Taylor series: 5.0 8 19.0065551524155296 19.0065778087482116 0.0001192025882298% ✔ 5.0 9 21.2426175047498660 21.2426457862480049 0.0001331354786194% ✔ Test Summary: | Pass Total Time -∫ψₙ*Hψₙdx = <ψₙ|H|ψₙ> = Eₙ | 40 40 0.6s +∫ψₙ*Hψₙdx = <ψₙ|H|ψₙ> = Eₙ | 40 40 1.4s ``` diff --git a/docs/src/HydrogenAtom.md b/docs/src/HydrogenAtom.md index 1483bcc..fd9289d 100644 --- a/docs/src/HydrogenAtom.md +++ b/docs/src/HydrogenAtom.md @@ -345,7 +345,7 @@ include("../../../test/HydrogenAtom.jl") ```math \begin{aligned} P_{2}^{0}(x) - = \frac{1}{8} \frac{\mathrm{d}^{2}}{\mathrm{d}x^{2}} \left( -1 + x^{2} \right)^{2} + = \frac{1}{8} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \left( -1 + x^{2} \right)^{2} &= \frac{-1}{2} + \frac{3}{2} x^{2} \\ &= \frac{-1}{2} + \frac{3}{2} x^{2} \end{aligned} @@ -355,7 +355,7 @@ include("../../../test/HydrogenAtom.jl") ```math \begin{aligned} P_{2}^{1}(x) - = \left( 1 - x^{2} \right)^{\frac{1}{2}} \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{8} \frac{\mathrm{d}^{2}}{\mathrm{d}x^{2}} \left( -1 + x^{2} \right)^{2} + = \left( 1 - x^{2} \right)^{\frac{1}{2}} \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{8} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \left( -1 + x^{2} \right)^{2} &= 3 \left( 1 - x^{2} \right)^{\frac{1}{2}} x \\ &= 3 \left( 1 - x^{2} \right)^{\frac{1}{2}} x \end{aligned} @@ -365,7 +365,7 @@ include("../../../test/HydrogenAtom.jl") ```math \begin{aligned} P_{2}^{2}(x) - = \left( 1 - x^{2} \right) \frac{\mathrm{d}^{2}}{\mathrm{d}x^{2}} \frac{1}{8} \frac{\mathrm{d}^{2}}{\mathrm{d}x^{2}} \left( -1 + x^{2} \right)^{2} + = \left( 1 - x^{2} \right) \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{8} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \left( -1 + x^{2} \right)^{2} &= 3 - 3 x^{2} \\ &= 3 - 3 x^{2} \end{aligned} @@ -375,7 +375,7 @@ include("../../../test/HydrogenAtom.jl") ```math \begin{aligned} P_{3}^{0}(x) - = \frac{1}{48} \frac{\mathrm{d}^{3}}{\mathrm{d}x^{3}} \left( -1 + x^{2} \right)^{3} + = \frac{1}{48} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \left( -1 + x^{2} \right)^{3} &= - \frac{3}{2} x + \frac{5}{2} x^{3} \\ &= - \frac{3}{2} x + \frac{5}{2} x^{3} \end{aligned} @@ -385,9 +385,9 @@ include("../../../test/HydrogenAtom.jl") ```math \begin{aligned} P_{3}^{1}(x) - = \left( 1 - x^{2} \right)^{\frac{1}{2}} \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{48} \frac{\mathrm{d}^{3}}{\mathrm{d}x^{3}} \left( -1 + x^{2} \right)^{3} - &= - \frac{3}{2} \left( 1 - x^{2} \right)^{\frac{1}{2}} + \frac{15}{2} \left( 1 - x^{2} \right)^{\frac{1}{2}} x^{2} \\ - &= - \frac{3}{2} \left( 1 - x^{2} \right)^{\frac{1}{2}} + \frac{15}{2} \left( 1 - x^{2} \right)^{\frac{1}{2}} x^{2} + = \left( 1 - x^{2} \right)^{\frac{1}{2}} \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{48} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \left( -1 + x^{2} \right)^{3} + &= - \frac{3}{2} \left( 1 - x^{2} \right)^{\frac{1}{2}} + \frac{15}{2} x^{2} \left( 1 - x^{2} \right)^{\frac{1}{2}} \\ + &= - \frac{3}{2} \left( 1 - x^{2} \right)^{\frac{1}{2}} + \frac{15}{2} x^{2} \left( 1 - x^{2} \right)^{\frac{1}{2}} \end{aligned} ``` @@ -395,7 +395,7 @@ include("../../../test/HydrogenAtom.jl") ```math \begin{aligned} P_{3}^{2}(x) - = \left( 1 - x^{2} \right) \frac{\mathrm{d}^{2}}{\mathrm{d}x^{2}} \frac{1}{48} \frac{\mathrm{d}^{3}}{\mathrm{d}x^{3}} \left( -1 + x^{2} \right)^{3} + = \left( 1 - x^{2} \right) \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{48} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \left( -1 + x^{2} \right)^{3} &= 15 x - 15 x^{3} \\ &= 15 x - 15 x^{3} \end{aligned} @@ -405,7 +405,7 @@ include("../../../test/HydrogenAtom.jl") ```math \begin{aligned} P_{3}^{3}(x) - = \left( 1 - x^{2} \right)^{\frac{3}{2}} \frac{\mathrm{d}^{3}}{\mathrm{d}x^{3}} \frac{1}{48} \frac{\mathrm{d}^{3}}{\mathrm{d}x^{3}} \left( -1 + x^{2} \right)^{3} + = \left( 1 - x^{2} \right)^{\frac{3}{2}} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{48} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \left( -1 + x^{2} \right)^{3} &= 15 \left( 1 - x^{2} \right)^{\frac{3}{2}} \\ &= 15 \left( 1 - x^{2} \right)^{\frac{3}{2}} \end{aligned} @@ -415,7 +415,7 @@ include("../../../test/HydrogenAtom.jl") ```math \begin{aligned} P_{4}^{0}(x) - = \frac{1}{384} \frac{\mathrm{d}^{4}}{\mathrm{d}x^{4}} \left( -1 + x^{2} \right)^{4} + = \frac{1}{384} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \left( -1 + x^{2} \right)^{4} &= \frac{3}{8} - \frac{15}{4} x^{2} + \frac{35}{8} x^{4} \\ &= \frac{3}{8} - \frac{15}{4} x^{2} + \frac{35}{8} x^{4} \end{aligned} @@ -425,9 +425,9 @@ include("../../../test/HydrogenAtom.jl") ```math \begin{aligned} P_{4}^{1}(x) - = \left( 1 - x^{2} \right)^{\frac{1}{2}} \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{384} \frac{\mathrm{d}^{4}}{\mathrm{d}x^{4}} \left( -1 + x^{2} \right)^{4} - &= - \frac{15}{2} \left( 1 - x^{2} \right)^{\frac{1}{2}} x + \frac{35}{2} \left( 1 - x^{2} \right)^{\frac{1}{2}} x^{3} \\ - &= - \frac{15}{2} \left( 1 - x^{2} \right)^{\frac{1}{2}} x + \frac{35}{2} \left( 1 - x^{2} \right)^{\frac{1}{2}} x^{3} + = \left( 1 - x^{2} \right)^{\frac{1}{2}} \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{384} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \left( -1 + x^{2} \right)^{4} + &= - \frac{15}{2} \left( 1 - x^{2} \right)^{\frac{1}{2}} x + \frac{35}{2} x^{3} \left( 1 - x^{2} \right)^{\frac{1}{2}} \\ + &= - \frac{15}{2} \left( 1 - x^{2} \right)^{\frac{1}{2}} x + \frac{35}{2} x^{3} \left( 1 - x^{2} \right)^{\frac{1}{2}} \end{aligned} ``` @@ -435,7 +435,7 @@ include("../../../test/HydrogenAtom.jl") ```math \begin{aligned} P_{4}^{2}(x) - = \left( 1 - x^{2} \right) \frac{\mathrm{d}^{2}}{\mathrm{d}x^{2}} \frac{1}{384} \frac{\mathrm{d}^{4}}{\mathrm{d}x^{4}} \left( -1 + x^{2} \right)^{4} + = \left( 1 - x^{2} \right) \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{384} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \left( -1 + x^{2} \right)^{4} &= \frac{-15}{2} + 60 x^{2} - \frac{105}{2} x^{4} \\ &= \frac{-15}{2} + 60 x^{2} - \frac{105}{2} x^{4} \end{aligned} @@ -445,7 +445,7 @@ include("../../../test/HydrogenAtom.jl") ```math \begin{aligned} P_{4}^{3}(x) - = \left( 1 - x^{2} \right)^{\frac{3}{2}} \frac{\mathrm{d}^{3}}{\mathrm{d}x^{3}} \frac{1}{384} \frac{\mathrm{d}^{4}}{\mathrm{d}x^{4}} \left( -1 + x^{2} \right)^{4} + = \left( 1 - x^{2} \right)^{\frac{3}{2}} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{384} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \left( -1 + x^{2} \right)^{4} &= 105 \left( 1 - x^{2} \right)^{\frac{3}{2}} x \\ &= 105 \left( 1 - x^{2} \right)^{\frac{3}{2}} x \end{aligned} @@ -455,15 +455,15 @@ include("../../../test/HydrogenAtom.jl") ```math \begin{aligned} P_{4}^{4}(x) - = \left( 1 - x^{2} \right)^{2} \frac{\mathrm{d}^{4}}{\mathrm{d}x^{4}} \frac{1}{384} \frac{\mathrm{d}^{4}}{\mathrm{d}x^{4}} \left( -1 + x^{2} \right)^{4} + = \left( 1 - x^{2} \right)^{2} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{384} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \left( -1 + x^{2} \right)^{4} &= 105 \left( 1 - x^{2} \right)^{2} \\ &= 105 \left( 1 - x^{2} \right)^{2} \end{aligned} ``` ``` -Test Summary: | Pass Total Time -Pₙᵐ(x) = √(1-x²)ᵐ dᵐ/dxᵐ Pₙ(x); Pₙ(x) = 1/(2ⁿn!) dⁿ/dxⁿ (x²-1)ⁿ | 15 15 17.3s +Test Summary: | Pass Total Time +Pₙᵐ(x) = √(1-x²)ᵐ dᵐ/dxᵐ Pₙ(x); Pₙ(x) = 1/(2ⁿn!) dⁿ/dxⁿ (x²-1)ⁿ | 15 15 1.9s ``` #### Normalization & Orthogonality of $P_n^m(x)$ @@ -829,7 +829,7 @@ Pₙᵐ(x) = √(1-x²)ᵐ dᵐ/dxᵐ Pₙ(x); Pₙ(x) = 1/(2ⁿn!) dⁿ/dxⁿ ( 5 9 8 -0.0000000013969839 0.0000000000000000 0.0000000000000000% ✔ 5 9 9 382360926.3157894611358643 382360926.3157894611358643 0.0000000000000000% ✔ Test Summary: | Pass Total Time -∫Pᵢᵐ(x)Pⱼᵐ(x)dx = 2(j+m)!/(2j+1)(j-m)! δᵢⱼ | 355 355 1.0s +∫Pᵢᵐ(x)Pⱼᵐ(x)dx = 2(j+m)!/(2j+1)(j-m)! δᵢⱼ | 355 355 1.5s ``` #### Normalization & Orthogonality of $Y_{lm}(\theta,\varphi)$ @@ -925,7 +925,7 @@ Y_{lm}(\theta,\varphi)^* Y_{l'm'}(\theta,\varphi) \sin(\theta) 2 2 2 1 0.0000000000000000 0.0000000000000000 0.0000000000000000% ✔ 2 2 2 2 1.0000000000000002 1.0000000000000000 0.0000000000000222% ✔ Test Summary: | Pass Total Time -∫Yₗ₁ₘ₁(θ,φ)Yₗ₂ₘ₂(θ,φ)sinθdθdφ = δₗ₁ₗ₂δₘ₁ₘ₂ | 81 81 2.8s +∫Yₗ₁ₘ₁(θ,φ)Yₗ₂ₘ₂(θ,φ)sinθdθdφ = δₗ₁ₗ₂δₘ₁ₘ₂ | 81 81 3.1s ``` #### Associated Laguerre Polynomials $L_n^{k}(x)$ @@ -944,7 +944,7 @@ Test Summary: | Pass Total Time ```math \begin{aligned} L_{0}^{0}(x) - = e^{x} e^{ - x} + = e^{ - x} e^{x} &= 1 \\ &= 1 \\ &= 1 @@ -955,7 +955,7 @@ Test Summary: | Pass Total Time ```math \begin{aligned} L_{1}^{0}(x) - = e^{x} \frac{\mathrm{d}}{\mathrm{d}x} x e^{ - x} + = \frac{\mathrm{d}}{\mathrm{d}x} x e^{ - x} e^{x} &= 1 - x \\ &= 1 - x \\ &= 1 - x @@ -966,7 +966,7 @@ Test Summary: | Pass Total Time ```math \begin{aligned} L_{1}^{1}(x) - = \frac{\mathrm{d}}{\mathrm{d}x} e^{x} \frac{\mathrm{d}}{\mathrm{d}x} x e^{ - x} + = \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x e^{ - x} e^{x} &= -1 \\ &= -1 \\ &= -1 @@ -977,10 +977,10 @@ Test Summary: | Pass Total Time ```math \begin{aligned} L_{2}^{0}(x) - = \frac{1}{2} e^{x} \frac{\mathrm{d}^{2}}{\mathrm{d}x^{2}} x^{2} e^{ - x} - &= 1 + \frac{1}{2} x^{2} - 2 x \\ - &= 1 + \frac{1}{2} x^{2} - 2 x \\ - &= 1 + \frac{1}{2} x^{2} - 2 x + = \frac{1}{2} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{2} e^{ - x} e^{x} + &= 1 - 2 x + \frac{1}{2} x^{2} \\ + &= 1 - 2 x + \frac{1}{2} x^{2} \\ + &= 1 - 2 x + \frac{1}{2} x^{2} \end{aligned} ``` @@ -988,7 +988,7 @@ Test Summary: | Pass Total Time ```math \begin{aligned} L_{2}^{1}(x) - = \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{2} e^{x} \frac{\mathrm{d}^{2}}{\mathrm{d}x^{2}} x^{2} e^{ - x} + = \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{2} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{2} e^{ - x} e^{x} &= -2 + x \\ &= -2 + x \\ &= -2 + x @@ -999,7 +999,7 @@ Test Summary: | Pass Total Time ```math \begin{aligned} L_{2}^{2}(x) - = \frac{\mathrm{d}^{2}}{\mathrm{d}x^{2}} \frac{1}{2} e^{x} \frac{\mathrm{d}^{2}}{\mathrm{d}x^{2}} x^{2} e^{ - x} + = \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{2} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{2} e^{ - x} e^{x} &= 1 \\ &= 1 \\ &= 1 @@ -1010,10 +1010,10 @@ Test Summary: | Pass Total Time ```math \begin{aligned} L_{3}^{0}(x) - = \frac{1}{6} e^{x} \frac{\mathrm{d}^{3}}{\mathrm{d}x^{3}} x^{3} e^{ - x} - &= 1 + \frac{3}{2} x^{2} - \frac{1}{6} x^{3} - 3 x \\ - &= 1 + \frac{3}{2} x^{2} - \frac{1}{6} x^{3} - 3 x \\ - &= 1 + \frac{3}{2} x^{2} - \frac{1}{6} x^{3} - 3 x + = \frac{1}{6} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{3} e^{ - x} e^{x} + &= 1 - 3 x + \frac{3}{2} x^{2} - \frac{1}{6} x^{3} \\ + &= 1 - 3 x + \frac{3}{2} x^{2} - \frac{1}{6} x^{3} \\ + &= 1 - 3 x + \frac{3}{2} x^{2} - \frac{1}{6} x^{3} \end{aligned} ``` @@ -1021,10 +1021,10 @@ Test Summary: | Pass Total Time ```math \begin{aligned} L_{3}^{1}(x) - = \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{6} e^{x} \frac{\mathrm{d}^{3}}{\mathrm{d}x^{3}} x^{3} e^{ - x} - &= -3 - \frac{1}{2} x^{2} + 3 x \\ - &= -3 - \frac{1}{2} x^{2} + 3 x \\ - &= -3 - \frac{1}{2} x^{2} + 3 x + = \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{6} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{3} e^{ - x} e^{x} + &= -3 + 3 x - \frac{1}{2} x^{2} \\ + &= -3 + 3 x - \frac{1}{2} x^{2} \\ + &= -3 + 3 x - \frac{1}{2} x^{2} \end{aligned} ``` @@ -1032,7 +1032,7 @@ Test Summary: | Pass Total Time ```math \begin{aligned} L_{3}^{2}(x) - = \frac{\mathrm{d}^{2}}{\mathrm{d}x^{2}} \frac{1}{6} e^{x} \frac{\mathrm{d}^{3}}{\mathrm{d}x^{3}} x^{3} e^{ - x} + = \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{6} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{3} e^{ - x} e^{x} &= 3 - x \\ &= 3 - x \\ &= 3 - x @@ -1043,7 +1043,7 @@ Test Summary: | Pass Total Time ```math \begin{aligned} L_{3}^{3}(x) - = \frac{\mathrm{d}^{3}}{\mathrm{d}x^{3}} \frac{1}{6} e^{x} \frac{\mathrm{d}^{3}}{\mathrm{d}x^{3}} x^{3} e^{ - x} + = \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{6} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{3} e^{ - x} e^{x} &= -1 \\ &= -1 \\ &= -1 @@ -1054,10 +1054,10 @@ Test Summary: | Pass Total Time ```math \begin{aligned} L_{4}^{0}(x) - = \frac{1}{24} e^{x} \frac{\mathrm{d}^{4}}{\mathrm{d}x^{4}} x^{4} e^{ - x} - &= 1 + 3 x^{2} + \frac{1}{24} x^{4} - \frac{2}{3} x^{3} - 4 x \\ - &= 1 + 3 x^{2} + \frac{1}{24} x^{4} - \frac{2}{3} x^{3} - 4 x \\ - &= 1 + 3 x^{2} + \frac{1}{24} x^{4} - \frac{2}{3} x^{3} - 4 x + = \frac{1}{24} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{4} e^{ - x} e^{x} + &= 1 - 4 x + 3 x^{2} - \frac{2}{3} x^{3} + \frac{1}{24} x^{4} \\ + &= 1 - 4 x + 3 x^{2} - \frac{2}{3} x^{3} + \frac{1}{24} x^{4} \\ + &= 1 - 4 x + 3 x^{2} - \frac{2}{3} x^{3} + \frac{1}{24} x^{4} \end{aligned} ``` @@ -1065,10 +1065,10 @@ Test Summary: | Pass Total Time ```math \begin{aligned} L_{4}^{1}(x) - = \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{24} e^{x} \frac{\mathrm{d}^{4}}{\mathrm{d}x^{4}} x^{4} e^{ - x} - &= -4 - 2 x^{2} + \frac{1}{6} x^{3} + 6 x \\ - &= -4 - 2 x^{2} + \frac{1}{6} x^{3} + 6 x \\ - &= -4 - 2 x^{2} + \frac{1}{6} x^{3} + 6 x + = \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{24} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{4} e^{ - x} e^{x} + &= -4 + 6 x - 2 x^{2} + \frac{1}{6} x^{3} \\ + &= -4 + 6 x - 2 x^{2} + \frac{1}{6} x^{3} \\ + &= -4 + 6 x - 2 x^{2} + \frac{1}{6} x^{3} \end{aligned} ``` @@ -1076,10 +1076,10 @@ Test Summary: | Pass Total Time ```math \begin{aligned} L_{4}^{2}(x) - = \frac{\mathrm{d}^{2}}{\mathrm{d}x^{2}} \frac{1}{24} e^{x} \frac{\mathrm{d}^{4}}{\mathrm{d}x^{4}} x^{4} e^{ - x} - &= 6 + \frac{1}{2} x^{2} - 4 x \\ - &= 6 + \frac{1}{2} x^{2} - 4 x \\ - &= 6 + \frac{1}{2} x^{2} - 4 x + = \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{24} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{4} e^{ - x} e^{x} + &= 6 - 4 x + \frac{1}{2} x^{2} \\ + &= 6 - 4 x + \frac{1}{2} x^{2} \\ + &= 6 - 4 x + \frac{1}{2} x^{2} \end{aligned} ``` @@ -1087,7 +1087,7 @@ Test Summary: | Pass Total Time ```math \begin{aligned} L_{4}^{3}(x) - = \frac{\mathrm{d}^{3}}{\mathrm{d}x^{3}} \frac{1}{24} e^{x} \frac{\mathrm{d}^{4}}{\mathrm{d}x^{4}} x^{4} e^{ - x} + = \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{24} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{4} e^{ - x} e^{x} &= -4 + x \\ &= -4 + x \\ &= -4 + x @@ -1098,7 +1098,7 @@ Test Summary: | Pass Total Time ```math \begin{aligned} L_{4}^{4}(x) - = \frac{\mathrm{d}^{4}}{\mathrm{d}x^{4}} \frac{1}{24} e^{x} \frac{\mathrm{d}^{4}}{\mathrm{d}x^{4}} x^{4} e^{ - x} + = \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{1}{24} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{4} e^{ - x} e^{x} &= 1 \\ &= 1 \\ &= 1 @@ -1107,7 +1107,7 @@ Test Summary: | Pass Total Time ``` Test Summary: | Pass Total Time -Lₙᵏ(x) = dᵏ/dxᵏ Lₙ(x); Lₙ(x) = 1/(n!) eˣ dⁿ/dxⁿ e⁻ˣ xⁿ | 15 15 5.8s +Lₙᵏ(x) = dᵏ/dxᵏ Lₙ(x); Lₙ(x) = 1/(n!) eˣ dⁿ/dxⁿ e⁻ˣ xⁿ | 15 15 0.9s ``` #### Normalization & Orthogonality of $L_n^{k}(x)$ @@ -1324,7 +1324,7 @@ Replace $n+k$ with $n$ for [the definition of Wolfram MathWorld](https://mathwor 7 7 6 5039.9999999999854481 5040.0000000000000000 0.0000000000002887% ✔ 7 7 7 5040.0000000000000000 5040.0000000000000000 0.0000000000000000% ✔ Test Summary: | Pass Total Time -∫exp(-x)xᵏLᵢᵏ(x)Lⱼᵏ(x)dx = (2i+k)!/(i+k)! δᵢⱼ | 204 204 0.7s +∫exp(-x)xᵏLᵢᵏ(x)Lⱼᵏ(x)dx = (2i+k)!/(i+k)! δᵢⱼ | 204 204 1.4s ``` #### Normalization of $R_{nl}(r)$ @@ -1380,7 +1380,7 @@ Test Summary: | Pass Total Time 9 7 1.0000000000000007 1.0000000000000000 0.0000000000000666% ✔ 9 8 0.9999999999999994 1.0000000000000000 0.0000000000000555% ✔ Test Summary: | Pass Total Time -∫|Rₙₗ(r)|²r²dr = δₙ₁ₙ₂δₗ₁ₗ₂ | 45 45 0.6s +∫|Rₙₗ(r)|²r²dr = δₙ₁ₙ₂δₗ₁ₗ₂ | 45 45 1.1s ``` #### Expected Value of $r$ @@ -1444,7 +1444,7 @@ Reference: 9 7 93.5000000000000000 93.5000000000000000 0.0000000000000000% ✔ 9 8 85.4999999999999716 85.5000000000000000 0.0000000000000332% ✔ Test Summary: | Pass Total Time -∫r|Rₙₗ(r)|²r²dr = (a₀×mₑ/μ)/2Z × [3n²-l(l+1)]; 1/μ = 1/mₑ + 1/mₚ | 45 45 0.4s +∫r|Rₙₗ(r)|²r²dr = (a₀×mₑ/μ)/2Z × [3n²-l(l+1)]; 1/μ = 1/mₑ + 1/mₚ | 45 45 0.9s ``` #### Expected Value of $r^2$ @@ -1508,7 +1508,7 @@ Reference: 9 7 9638.9999999999909051 9639.0000000000000000 0.0000000000000944% ✔ 9 8 7694.9999999999981810 7695.0000000000000000 0.0000000000000236% ✔ Test Summary: | Pass Total Time -∫r²|Rₙₗ(r)|²r²dr = (a₀×mₑ/μ)²/2Z² × n²[5n²+1-3l(l+1)]; 1/μ = 1/mₑ + 1/mₚ | 45 45 0.5s +∫r²|Rₙₗ(r)|²r²dr = (a₀×mₑ/μ)²/2Z² × n²[5n²+1-3l(l+1)]; 1/μ = 1/mₑ + 1/mₚ | 45 45 1.0s ``` #### Virial Theorem @@ -1531,7 +1531,7 @@ The virial theorem $2\langle T \rangle + \langle V \rangle = 0$ and the definiti 9 -0.0123456790123456 -0.0123456790123457 0.0000000000002389% ✔ 10 -0.0100000000000004 -0.0100000000000000 0.0000000000036256% ✔ Test Summary: | Pass Total Time -<ψₙ|V|ψₙ> / 2 = Eₙ | 10 10 0.8s +<ψₙ|V|ψₙ> / 2 = Eₙ | 10 10 0.9s ``` #### Normalization & Orthogonality of $\psi_n(r,\theta,\varphi)$ @@ -1738,6 +1738,6 @@ Test Summary: | Pass Total Time 3 3 2 2 2 1 0.0000000000000000 0.0000000000000000 0.0000000000000000% ✔ 3 3 2 2 2 2 1.0003006285656155 1.0000000000000000 0.0300628565615524% ✔ Test Summary: | Pass Total Time -<ψₙ₁ₗ₁ₘ₁|ψₙ₂ₗ₂ₘ₂> = δₙ₁ₙ₂δₗ₁ₗ₂δₘ₁ₘ₂ | 196 196 27.4s +<ψₙ₁ₗ₁ₘ₁|ψₙ₂ₗ₂ₘ₂> = δₙ₁ₙ₂δₗ₁ₗ₂δₘ₁ₘ₂ | 196 196 26.8s ``` diff --git a/docs/src/InfinitePotentialWell.md b/docs/src/InfinitePotentialWell.md index 88db340..f611e80 100644 --- a/docs/src/InfinitePotentialWell.md +++ b/docs/src/InfinitePotentialWell.md @@ -239,7 +239,7 @@ include("../../../test/InfinitePotentialWell.jl") 10 9 0.0000000000000001 0.0000000000000000 0.0000000000000000% ✔ 10 10 1.0000000000000002 1.0000000000000000 0.0000000000000222% ✔ Test Summary: | Pass Total Time -<ψᵢ|ψⱼ> = ∫ψₙ*ψₙdx = δᵢⱼ | 100 100 2.3s +<ψᵢ|ψⱼ> = ∫ψₙ*ψₙdx = δᵢⱼ | 100 100 1.5s ``` #### Eigen Values @@ -386,7 +386,7 @@ are given by the sum of 2 Taylor series: 1.0 1.0 1.0 9 399.718711951912 399.718978244119 0.000066619856% ✔ 1.0 1.0 1.0 10 493.479814178266 493.480220054468 0.000082247714% ✔ Test Summary: | Pass Total Time -<ψₙ|H|ψₙ> = ∫ψₙ*Tψₙdx = Eₙ | 80 80 0.9s +<ψₙ|H|ψₙ> = ∫ψₙ*Tψₙdx = Eₙ | 80 80 1.2s ``` #### Expected Value of $x$ @@ -406,7 +406,7 @@ Reference: 1.0 1 0.5000000000000002 0.5000000000000000 0.0000000000000444% ✔ 7.0 1 3.5000000000000000 3.5000000000000000 0.0000000000000000% ✔ Test Summary: | Pass Total Time -<ψₙ|x|ψₙ> = L/2 | 4 4 0.4s +<ψₙ|x|ψₙ> = L/2 | 4 4 0.7s ``` #### Expected Value of $x^2$ @@ -425,7 +425,7 @@ Reference: 1.0 1 0.2826727415121645 0.2826727415121645 0.0000000000000196% ✔ 7.0 1 13.8509643340960604 13.8509643340960569 0.0000000000000256% ✔ Test Summary: | Pass Total Time -<ψₙ|x²|ψₙ> = 2L²/π³(π³/6-π/4) | 4 4 0.4s +<ψₙ|x²|ψₙ> = 2L²/π³(π³/6-π/4) | 4 4 0.5s ``` #### Expected Value of $p$ @@ -503,7 +503,7 @@ are given by the sum of 2 Taylor series: 1.0 1 0.0000000000001066 0.0000000000000000 0.0000000000000000% ✔ 7.0 1 0.0000000000000252 0.0000000000000000 0.0000000000000000% ✔ Test Summary: | Pass Total Time -<ψₙ|p|ψₙ> = ∫ψₙ*(-iℏd/dx)ψₙdx = 0 | 4 4 0.7s +<ψₙ|p|ψₙ> = ∫ψₙ*(-iℏd/dx)ψₙdx = 0 | 4 4 0.9s ``` #### Expected Value of $p^2$ diff --git a/docs/src/MorsePotential.md b/docs/src/MorsePotential.md index 3c37f59..3752f84 100644 --- a/docs/src/MorsePotential.md +++ b/docs/src/MorsePotential.md @@ -197,7 +197,7 @@ include("../../../test/MorsePotential.jl") ```math \begin{aligned} L_{0}^{(0)}(x) - = e^{x} e^{ - x} + = e^{ - x} e^{x} &= 1 \\ &= 1 \end{aligned} @@ -207,7 +207,7 @@ include("../../../test/MorsePotential.jl") ```math \begin{aligned} L_{1}^{(0)}(x) - = e^{x} \frac{\mathrm{d}}{\mathrm{d}x} x e^{ - x} + = \frac{\mathrm{d}}{\mathrm{d}x} x e^{ - x} e^{x} &= 1 - x \\ &= 1 - x \end{aligned} @@ -227,9 +227,9 @@ include("../../../test/MorsePotential.jl") ```math \begin{aligned} L_{2}^{(0)}(x) - = \frac{1}{2} e^{x} \frac{\mathrm{d}^{2}}{\mathrm{d}x^{2}} x^{2} e^{ - x} - &= 1 + \frac{1}{2} x^{2} - 2 x \\ - &= 1 + \frac{1}{2} x^{2} - 2 x + = \frac{1}{2} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{2} e^{ - x} e^{x} + &= 1 - 2 x + \frac{1}{2} x^{2} \\ + &= 1 - 2 x + \frac{1}{2} x^{2} \end{aligned} ``` @@ -237,9 +237,9 @@ include("../../../test/MorsePotential.jl") ```math \begin{aligned} L_{2}^{(1)}(x) - = \frac{\frac{1}{2} e^{x} \frac{\mathrm{d}^{2}}{\mathrm{d}x^{2}} x^{3} e^{ - x}}{x} - &= 3 + \frac{1}{2} x^{2} - 3 x \\ - &= 3 + \frac{1}{2} x^{2} - 3 x + = \frac{\frac{1}{2} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{3} e^{ - x} e^{x}}{x} + &= 3 - 3 x + \frac{1}{2} x^{2} \\ + &= 3 - 3 x + \frac{1}{2} x^{2} \end{aligned} ``` @@ -247,9 +247,9 @@ include("../../../test/MorsePotential.jl") ```math \begin{aligned} L_{2}^{(2)}(x) - = \frac{\frac{1}{2} e^{x} \frac{\mathrm{d}^{2}}{\mathrm{d}x^{2}} x^{4} e^{ - x}}{x^{2}} - &= 6 + \frac{1}{2} x^{2} - 4 x \\ - &= 6 + \frac{1}{2} x^{2} - 4 x + = \frac{\frac{1}{2} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{4} e^{ - x} e^{x}}{x^{2}} + &= 6 - 4 x + \frac{1}{2} x^{2} \\ + &= 6 - 4 x + \frac{1}{2} x^{2} \end{aligned} ``` @@ -257,9 +257,9 @@ include("../../../test/MorsePotential.jl") ```math \begin{aligned} L_{3}^{(0)}(x) - = \frac{1}{6} e^{x} \frac{\mathrm{d}^{3}}{\mathrm{d}x^{3}} x^{3} e^{ - x} - &= 1 + \frac{3}{2} x^{2} - \frac{1}{6} x^{3} - 3 x \\ - &= 1 + \frac{3}{2} x^{2} - \frac{1}{6} x^{3} - 3 x + = \frac{1}{6} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{3} e^{ - x} e^{x} + &= 1 - 3 x + \frac{3}{2} x^{2} - \frac{1}{6} x^{3} \\ + &= 1 - 3 x + \frac{3}{2} x^{2} - \frac{1}{6} x^{3} \end{aligned} ``` @@ -267,9 +267,9 @@ include("../../../test/MorsePotential.jl") ```math \begin{aligned} L_{3}^{(1)}(x) - = \frac{\frac{1}{6} e^{x} \frac{\mathrm{d}^{3}}{\mathrm{d}x^{3}} x^{4} e^{ - x}}{x} - &= 4 + 2 x^{2} - \frac{1}{6} x^{3} - 6 x \\ - &= 4 + 2 x^{2} - \frac{1}{6} x^{3} - 6 x + = \frac{\frac{1}{6} e^{x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{4} e^{ - x}}{x} + &= 4 - 6 x + 2 x^{2} - \frac{1}{6} x^{3} \\ + &= 4 - 6 x + 2 x^{2} - \frac{1}{6} x^{3} \end{aligned} ``` @@ -277,9 +277,9 @@ include("../../../test/MorsePotential.jl") ```math \begin{aligned} L_{3}^{(2)}(x) - = \frac{\frac{1}{6} e^{x} \frac{\mathrm{d}^{3}}{\mathrm{d}x^{3}} x^{5} e^{ - x}}{x^{2}} - &= 10 + \frac{5}{2} x^{2} - \frac{1}{6} x^{3} - 10 x \\ - &= 10 + \frac{5}{2} x^{2} - \frac{1}{6} x^{3} - 10 x + = \frac{\frac{1}{6} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{5} e^{ - x} e^{x}}{x^{2}} + &= 10 - 10 x + \frac{5}{2} x^{2} - \frac{1}{6} x^{3} \\ + &= 10 - 10 x + \frac{5}{2} x^{2} - \frac{1}{6} x^{3} \end{aligned} ``` @@ -287,9 +287,9 @@ include("../../../test/MorsePotential.jl") ```math \begin{aligned} L_{3}^{(3)}(x) - = \frac{\frac{1}{6} e^{x} \frac{\mathrm{d}^{3}}{\mathrm{d}x^{3}} x^{6} e^{ - x}}{x^{3}} - &= 20 + 3 x^{2} - \frac{1}{6} x^{3} - 15 x \\ - &= 20 + 3 x^{2} - \frac{1}{6} x^{3} - 15 x + = \frac{\frac{1}{6} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{6} e^{ - x} e^{x}}{x^{3}} + &= 20 - 15 x + 3 x^{2} - \frac{1}{6} x^{3} \\ + &= 20 - 15 x + 3 x^{2} - \frac{1}{6} x^{3} \end{aligned} ``` @@ -297,9 +297,9 @@ include("../../../test/MorsePotential.jl") ```math \begin{aligned} L_{4}^{(0)}(x) - = \frac{1}{24} e^{x} \frac{\mathrm{d}^{4}}{\mathrm{d}x^{4}} x^{4} e^{ - x} - &= 1 + 3 x^{2} + \frac{1}{24} x^{4} - \frac{2}{3} x^{3} - 4 x \\ - &= 1 + 3 x^{2} + \frac{1}{24} x^{4} - \frac{2}{3} x^{3} - 4 x + = \frac{1}{24} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{4} e^{ - x} e^{x} + &= 1 - 4 x + 3 x^{2} - \frac{2}{3} x^{3} + \frac{1}{24} x^{4} \\ + &= 1 - 4 x + 3 x^{2} - \frac{2}{3} x^{3} + \frac{1}{24} x^{4} \end{aligned} ``` @@ -307,9 +307,9 @@ include("../../../test/MorsePotential.jl") ```math \begin{aligned} L_{4}^{(1)}(x) - = \frac{\frac{1}{24} e^{x} \frac{\mathrm{d}^{4}}{\mathrm{d}x^{4}} x^{5} e^{ - x}}{x} - &= 5 + 5 x^{2} + \frac{1}{24} x^{4} - \frac{5}{6} x^{3} - 10 x \\ - &= 5 + 5 x^{2} + \frac{1}{24} x^{4} - \frac{5}{6} x^{3} - 10 x + = \frac{\frac{1}{24} e^{x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{5} e^{ - x}}{x} + &= 5 - 10 x + 5 x^{2} - \frac{5}{6} x^{3} + \frac{1}{24} x^{4} \\ + &= 5 - 10 x + 5 x^{2} - \frac{5}{6} x^{3} + \frac{1}{24} x^{4} \end{aligned} ``` @@ -317,9 +317,9 @@ include("../../../test/MorsePotential.jl") ```math \begin{aligned} L_{4}^{(2)}(x) - = \frac{\frac{1}{24} e^{x} \frac{\mathrm{d}^{4}}{\mathrm{d}x^{4}} x^{6} e^{ - x}}{x^{2}} - &= 15 + \frac{15}{2} x^{2} + \frac{1}{24} x^{4} - x^{3} - 20 x \\ - &= 15 + \frac{15}{2} x^{2} + \frac{1}{24} x^{4} - x^{3} - 20 x + = \frac{\frac{1}{24} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{6} e^{ - x} e^{x}}{x^{2}} + &= 15 - 20 x + \frac{15}{2} x^{2} - x^{3} + \frac{1}{24} x^{4} \\ + &= 15 - 20 x + \frac{15}{2} x^{2} - x^{3} + \frac{1}{24} x^{4} \end{aligned} ``` @@ -327,9 +327,9 @@ include("../../../test/MorsePotential.jl") ```math \begin{aligned} L_{4}^{(3)}(x) - = \frac{\frac{1}{24} e^{x} \frac{\mathrm{d}^{4}}{\mathrm{d}x^{4}} x^{7} e^{ - x}}{x^{3}} - &= 35 + \frac{21}{2} x^{2} + \frac{1}{24} x^{4} - \frac{7}{6} x^{3} - 35 x \\ - &= 35 + \frac{21}{2} x^{2} + \frac{1}{24} x^{4} - \frac{7}{6} x^{3} - 35 x + = \frac{\frac{1}{24} e^{x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{7} e^{ - x}}{x^{3}} + &= 35 - 35 x + \frac{21}{2} x^{2} - \frac{7}{6} x^{3} + \frac{1}{24} x^{4} \\ + &= 35 - 35 x + \frac{21}{2} x^{2} - \frac{7}{6} x^{3} + \frac{1}{24} x^{4} \end{aligned} ``` @@ -337,15 +337,15 @@ include("../../../test/MorsePotential.jl") ```math \begin{aligned} L_{4}^{(4)}(x) - = \frac{\frac{1}{24} e^{x} \frac{\mathrm{d}^{4}}{\mathrm{d}x^{4}} x^{8} e^{ - x}}{x^{4}} - &= 70 + 14 x^{2} + \frac{1}{24} x^{4} - \frac{4}{3} x^{3} - 56 x \\ - &= 70 + 14 x^{2} + \frac{1}{24} x^{4} - \frac{4}{3} x^{3} - 56 x + = \frac{\frac{1}{24} e^{x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} \frac{\mathrm{d}}{\mathrm{d}x} x^{8} e^{ - x}}{x^{4}} + &= 70 - 56 x + 14 x^{2} - \frac{4}{3} x^{3} + \frac{1}{24} x^{4} \\ + &= 70 - 56 x + 14 x^{2} - \frac{4}{3} x^{3} + \frac{1}{24} x^{4} \end{aligned} ``` ``` -Test Summary: | Pass Total Time -Lₙ⁽ᵅ⁾(x) = x⁻ᵅeˣ/n! dⁿ/dxⁿ xⁿ⁺ᵅe⁻ˣ | 15 15 7.8s +Test Summary: | Pass Total Time +Lₙ⁽ᵅ⁾(x) = x⁻ᵅeˣ/n! dⁿ/dxⁿ xⁿ⁺ᵅe⁻ˣ | 15 15 20.0s ``` #### Normalization & Orthogonality of $L_n^{(\alpha)}(x)$ @@ -869,7 +869,7 @@ Test Summary: | Pass Total Time 9 8 0.0000000000003093 0.0000000000000000 0.0000000000000000% ✔ 9 9 1.0000000000154354 1.0000000000000000 0.0000000015435431% ✔ Test Summary: | Pass Total Time -<ψᵢ|ψⱼ> = δᵢⱼ | 100 100 1.7s +<ψᵢ|ψⱼ> = δᵢⱼ | 100 100 1.9s ``` #### Eigen Values @@ -940,20 +940,20 @@ are given by the sum of 2 Taylor series: 0.10000 1 -0.0875766292083366 -0.0875766290728626 0.0000001546919476% ✔ 0.10000 2 -0.0782012653591236 -0.0782012650053099 0.0000004524398330% ✔ 0.10000 3 -0.0693565382661101 -0.0693565377016763 0.0000008138149329% ✔ -0.10000 4 -0.0610424487769010 -0.0610424471619618 0.0000026456004304% ✔ -0.10000 5 -0.0532589961311517 -0.0532589933861664 0.0000051540315631% ✔ -0.10000 6 -0.0460061778289177 -0.0460061763742900 0.0000031618096040% ✔ -0.10000 7 -0.0392839977431083 -0.0392839961263328 0.0000041156085192% ✔ -0.10000 8 -0.0330924678509620 -0.0330924526422947 0.0000459581146490% ✔ -0.10000 9 -0.0274314677918593 -0.0274315459221756 0.0002848192245706% ✔ +0.10000 4 -0.0610424487768959 -0.0610424471619618 0.0000026455920072% ✔ +0.10000 5 -0.0532589961311526 -0.0532589933861664 0.0000051540333741% ✔ +0.10000 6 -0.0460061778289117 -0.0460061763742900 0.0000031617965576% ✔ +0.10000 7 -0.0392839977431085 -0.0392839961263328 0.0000041156089608% ✔ +0.10000 8 -0.0330924678509606 -0.0330924526422947 0.0000459581104973% ✔ +0.10000 9 -0.0274314677918590 -0.0274315459221756 0.0002848192256583% ✔ 0.20000 0 -0.0953874611439631 -0.0953874610810323 0.0000000659738844% ✔ 0.20000 1 -0.0816891004273675 -0.0816891001758958 0.0000003078400078% ✔ 0.20000 2 -0.0690520133797856 -0.0690520127985975 0.0000008416671348% ✔ 0.20000 3 -0.0574761998667120 -0.0574761989491373 0.0000015964429232% ✔ 0.20000 4 -0.0469616603170172 -0.0469616586275153 0.0000035976196186% ✔ 0.20000 5 -0.0375083932021688 -0.0375083918337316 0.0000036483494226% ✔ -0.20000 6 -0.0291164003400069 -0.0291163985677860 0.0000060866763527% ✔ -0.20000 7 -0.0217856840623444 -0.0217856788296786 0.0000240188326428% ✔ +0.20000 6 -0.0291164003400053 -0.0291163985677860 0.0000060866708238% ✔ +0.20000 7 -0.0217856840623437 -0.0217856788296786 0.0000240188297604% ✔ 0.20000 8 -0.0155162375387778 -0.0155162326194094 0.0000317046571552% ✔ 0.20000 9 -0.0103080627546147 -0.0103080599369784 0.0000273343029443% ✔ 0.30000 0 -0.0937952146950324 -0.0937952146053093 0.0000000956584648% ✔ @@ -966,17 +966,17 @@ are given by the sum of 2 Taylor series: 0.30000 7 -0.0118311981022458 -0.0118311967467099 0.0000114573015073% ✔ 0.30000 8 -0.0064896942752905 -0.0064896925053676 0.0000272728303901% ✔ 0.30000 9 -0.0027401008929208 -0.0027400985557827 0.0000852939413987% ✔ -0.10273 0 -0.0974137779681661 -0.0974137779441826 0.0000000246202580% ✔ +0.10273 0 -0.0974137779674584 -0.0974137779441826 0.0000000238937717% ✔ 0.10273 1 -0.0873809242053181 -0.0873809240676091 0.0000001575961943% ✔ 0.10273 2 -0.0778931751450495 -0.0778931747885570 0.0000004576684890% ✔ 0.10273 3 -0.0689505306599348 -0.0689505301070264 0.0000008018914211% ✔ 0.10273 4 -0.0605529890953712 -0.0605529900230172 0.0000015319574295% ✔ -0.10273 5 -0.0527005572549315 -0.0527005545365296 0.0000051582036490% ✔ -0.10273 6 -0.0453932228176848 -0.0453932236475634 0.0000018281991459% ✔ -0.10273 7 -0.0386310171570861 -0.0386309973561186 0.0000512566820760% ✔ -0.10273 8 -0.0324138862460414 -0.0324138756621953 0.0000326522081163% ✔ -0.10273 9 -0.0267420183757886 -0.0267418585657935 0.0005976024244662% ✔ +0.10273 5 -0.0527005572549377 -0.0527005545365296 0.0000051582153937% ✔ +0.10273 6 -0.0453932228176823 -0.0453932236475634 0.0000018282046030% ✔ +0.10273 7 -0.0386310171570861 -0.0386309973561186 0.0000512566822197% ✔ +0.10273 8 -0.0324138862460601 -0.0324138756621953 0.0000326522656802% ✔ +0.10273 9 -0.0267420183757886 -0.0267418585657935 0.0005976024244533% ✔ Test Summary: | Pass Total Time -<ψₙ|H|ψₙ> = ∫ψₙ*Hψₙdx = Eₙ | 40 40 3.7s +<ψₙ|H|ψₙ> = ∫ψₙ*Hψₙdx = Eₙ | 40 40 4.5s ``` diff --git a/docs/src/assets/fig/HarmonicOscillator_5_1.png b/docs/src/assets/fig/HarmonicOscillator_5_1.png index 41c16acc450ed8d7f657aa976d31dfb62820f5a3..918db39c4c5d0d5f46809e19ec21f8f3644229f6 100644 GIT binary patch literal 60130 zcmb4q1y@{6)9v8y9yCC3f&_;E!QF#9!QI^(_Y5CDMigNFqF=g*^*1o#iEp|rRN;N#y< zPG@lf06+$i6#1dz20YC))z{ja2Yo!~%35k{tVX-??W9QxNl1{P(*zN41Sbp8G8RTA zuPccmIZfgHp-WVRmn5q|Ckte#BdT`0=nSd&e$jaW_odg~N+bSD2G`_;vcp{@g@)Qe 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antiq(model; parameters...) # check existence of model if model ∉ models - throw(ErrorException("\`:$(model)\` is not in the supported models $(models).")) + throw(ErrorException("\`:$(model)\` is not in the list of supported models $(models).")) end # load source code file if Sys.iswindows() diff --git a/src/HarmonicOscillator.jl b/src/HarmonicOscillator.jl index 620dcd8..bfe3e32 100644 --- a/src/HarmonicOscillator.jl +++ b/src/HarmonicOscillator.jl @@ -19,6 +19,6 @@ module HarmonicOscillator end # Hermite polynomials - H(x; n=0) = factorial(n) * sum(m -> (-1)^m // (factorial(m) * factorial(n-2*m)) * (2*x)^(n-2*m), 0:Int(floor(n/2))) + H(x; n=0) = factorial(n) * sum(i -> (-1)^i // (factorial(i) * factorial(n-2*i)) * (2*x)^(n-2*i), 0:Int(floor(n/2))) end diff --git a/test/HarmonicOscillator.jl b/test/HarmonicOscillator.jl index 2dde7c2..0377be7 100644 --- a/test/HarmonicOscillator.jl +++ b/test/HarmonicOscillator.jl @@ -24,7 +24,7 @@ println(raw""" ``` """) -@testset "Hₙ(x) = (-1)ⁿ exp(x²) dⁿ/dxⁿ　exp(-x²) = ..." begin +@testset "Hₙ(x) = (-1)ⁿ exp(x²) dⁿ/dxⁿ exp(-x²) = ..." begin for n in 0:9 # Rodrigues' formula @variables x @@ -36,7 +36,7 @@ println(raw""" e = simplify(d, expand=true) # simplify # closed-form eq1 = latexify(e, env=:raw) - eq2 = latexify(HO.H(x, n=n), env=:raw) + eq2 = latexify(simplify(HO.H(x, n=n), expand=true), env=:raw) # judge acceptance = (eq1 == eq2) println("``n=$n:`` ", acceptance ? "✔" : "✗")