Skip to content

Commit

Permalink
build based on 11441b1
Browse files Browse the repository at this point in the history
  • Loading branch information
Documenter.jl committed Nov 29, 2023
1 parent 51965c9 commit ed98869
Show file tree
Hide file tree
Showing 17 changed files with 116 additions and 1,036 deletions.
2 changes: 1 addition & 1 deletion dev/.documenter-siteinfo.json
View file
Original file line number Diff line number Diff line change
@@ -1 +1 @@
{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-11-29T21:33:28","documenter_version":"1.2.0"}}
{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-11-29T23:37:31","documenter_version":"1.2.0"}}
367 changes: 18 additions & 349 deletions dev/HarmonicOscillator/index.html
View file

Large diffs are not rendered by default.

84 changes: 42 additions & 42 deletions dev/HydrogenAtom/index.html
View file

Large diffs are not rendered by default.

14 changes: 7 additions & 7 deletions dev/InfinitePotentialWell/index.html
View file
Original file line number Diff line number Diff line change
Expand Up @@ -25,7 +25,7 @@
plot!(x -> IPW.ψ(x, n=4), label="n=4", lw=2)
plot!(x -&gt; IPW.ψ(x, n=5), label=&quot;n=5&quot;, lw=2)</code></pre><p><img src="../assets/fig/InfinitePotentialWell_4_1.png" alt/></p><p>Potential energy curve, Energy levels, Wave functions:</p><pre><code class="language-julia hljs">L = 1
using Plots
plot(xlim=(-0.5,1.5), ylim=(-5,140), xlabel=&quot;\$x\$&quot;, ylabel=&quot;\$V(x),~E_n,~\\psi_n(x)\\times5+E_n\$&quot;, size=(480,400), dpi=400)
plot(xlim=(-0.5,1.5), ylim=(-5,140), xlabel=&quot;\$x\$&quot;, ylabel=&quot;\$V(x),~E_n,~\\psi_n(x)\\times5+E_n\$&quot;, size=(480,400), dpi=300)
for n in 1:5
# energy
plot!([0,L], fill(IPW.E(n=n,L=L),2), lc=:black, lw=2, label=&quot;&quot;)
Expand Down Expand Up @@ -135,7 +135,7 @@
10 9 0.0000000000000001 0.0000000000000000 0.0000000000000000% ✔
10 10 1.0000000000000002 1.0000000000000000 0.0000000000000222% ✔
Test Summary: | Pass Total Time
&lt;ψᵢ|ψⱼ&gt; = ∫ψₙ*ψₙdx = δᵢⱼ | 100 100 1.5s</code></pre><h4 id="Eigen-Values-2"><a class="docs-heading-anchor" href="#Eigen-Values-2">Eigen Values</a><a class="docs-heading-anchor-permalink" href="#Eigen-Values-2" title="Permalink"></a></h4><p class="math-container">\[ \begin{aligned}
&lt;ψᵢ|ψⱼ&gt; = ∫ψₙ*ψₙdx = δᵢⱼ | 100 100 2.3s</code></pre><h4 id="Eigen-Values-2"><a class="docs-heading-anchor" href="#Eigen-Values-2">Eigen Values</a><a class="docs-heading-anchor-permalink" href="#Eigen-Values-2" title="Permalink"></a></h4><p class="math-container">\[ \begin{aligned}
E_n
&amp;= \int_0^L \psi^\ast_n(x) \hat{H} \psi_n(x) ~\mathrm{d}x \\
&amp;= \int_0^L \psi^\ast_n(x) \left[ \hat{V} + \hat{T} \right] \psi(x) ~\mathrm{d}x \\
Expand Down Expand Up @@ -261,15 +261,15 @@
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
&lt;ψₙ|H|ψₙ&gt; = ∫ψₙ*Tψₙdx = Eₙ | 80 80 1.2s</code></pre><h4 id="Expected-Value-of-x"><a class="docs-heading-anchor" href="#Expected-Value-of-x">Expected Value of <span>$x$</span></a><a id="Expected-Value-of-x-1"></a><a class="docs-heading-anchor-permalink" href="#Expected-Value-of-x" title="Permalink"></a></h4><p class="math-container">\[\langle x \rangle_{n=1}
&lt;ψₙ|H|ψₙ&gt; = ∫ψₙ*Tψₙdx = Eₙ | 80 80 0.9s</code></pre><h4 id="Expected-Value-of-x"><a class="docs-heading-anchor" href="#Expected-Value-of-x">Expected Value of <span>$x$</span></a><a id="Expected-Value-of-x-1"></a><a class="docs-heading-anchor-permalink" href="#Expected-Value-of-x" title="Permalink"></a></h4><p class="math-container">\[\langle x \rangle_{n=1}
= \int_{0}^{L} \psi_1^\ast(x) \hat{x} \psi_1(x) ~\mathrm{d}x
= \frac{2(2a)^2}{\pi^3} \left( \frac{\pi^3}{6} - \frac{\pi}{4} \right)\]</p><p>for only <span>$n=1$</span>.</p><p>Reference:</p><ul><li><a href="https://phys.libretexts.org/Bookshelves/Modern_Physics/Book%3A_Spiral_Modern_Physics_(D&#39;Alessandris)/6%3A_The_Schrodinger_Equation/6.4%3A_Expectation_Values_Observables_and_Uncertainty">LibreTexts PHYSICS, 6.4: Expectation Values, Observables, and Uncertainty</a></li></ul><pre><code class="nohighlight hljs"> L n numerical analytical |error|
0.1 1 0.0500000000000000 0.0500000000000000 0.0000000000000278% ✔
0.5 1 0.2500000000000000 0.2500000000000000 0.0000000000000000% ✔
1.0 1 0.5000000000000002 0.5000000000000000 0.0000000000000444% ✔
7.0 1 3.5000000000000000 3.5000000000000000 0.0000000000000000% ✔
Test Summary: | Pass Total Time
&lt;ψₙ|x|ψₙ&gt; = L/2 | 4 4 0.7s</code></pre><h4 id="Expected-Value-of-x2"><a class="docs-heading-anchor" href="#Expected-Value-of-x2">Expected Value of <span>$x^2$</span></a><a id="Expected-Value-of-x2-1"></a><a class="docs-heading-anchor-permalink" href="#Expected-Value-of-x2" title="Permalink"></a></h4><p class="math-container">\[\langle x^2 \rangle_{n=1}
&lt;ψₙ|x|ψₙ&gt; = L/2 | 4 4 0.5s</code></pre><h4 id="Expected-Value-of-x2"><a class="docs-heading-anchor" href="#Expected-Value-of-x2">Expected Value of <span>$x^2$</span></a><a id="Expected-Value-of-x2-1"></a><a class="docs-heading-anchor-permalink" href="#Expected-Value-of-x2" title="Permalink"></a></h4><p class="math-container">\[\langle x^2 \rangle_{n=1}
= \int_{0}^{L} \psi_1^\ast(x) \hat{x}^2 \psi_1(x) ~\mathrm{d}x
= \frac{2(2a)^2}{\pi^3} \left( \frac{\pi^3}{6} - \frac{\pi}{4} \right)\]</p><p>Reference:</p><ul><li><a href="https://phys.libretexts.org/Bookshelves/Modern_Physics/Book%3A_Spiral_Modern_Physics_(D&#39;Alessandris)/6%3A_The_Schrodinger_Equation/6.4%3A_Expectation_Values_Observables_and_Uncertainty">LibreTexts PHYSICS, 6.4: Expectation Values, Observables, and Uncertainty</a></li></ul><pre><code class="nohighlight hljs"> L n numerical analytical |error|
0.1 1 0.0028267274151216 0.0028267274151216 0.0000000000000460% ✔
Expand Down Expand Up @@ -326,7 +326,7 @@
1.0 1 0.0000000000001066 0.0000000000000000 0.0000000000000000% ✔
7.0 1 0.0000000000000252 0.0000000000000000 0.0000000000000000% ✔
Test Summary: | Pass Total Time
&lt;ψₙ|p|ψₙ&gt; = ∫ψₙ*(-iℏd/dx)ψₙdx = 0 | 4 4 0.9s</code></pre><h4 id="Expected-Value-of-p2"><a class="docs-heading-anchor" href="#Expected-Value-of-p2">Expected Value of <span>$p^2$</span></a><a id="Expected-Value-of-p2-1"></a><a class="docs-heading-anchor-permalink" href="#Expected-Value-of-p2" title="Permalink"></a></h4><p class="math-container">\[\langle p^2 \rangle
&lt;ψₙ|p|ψₙ&gt; = ∫ψₙ*(-iℏd/dx)ψₙdx = 0 | 4 4 0.7s</code></pre><h4 id="Expected-Value-of-p2"><a class="docs-heading-anchor" href="#Expected-Value-of-p2">Expected Value of <span>$p^2$</span></a><a id="Expected-Value-of-p2-1"></a><a class="docs-heading-anchor-permalink" href="#Expected-Value-of-p2" title="Permalink"></a></h4><p class="math-container">\[\langle p^2 \rangle
= \int_{0}^{L} \psi_1^\ast(x) \hat{p}^2 \psi_1(x) ~\mathrm{d}x
= \frac{\pi^2\hbar^2}{L^2}\]</p><p>Reference:</p><ul><li><a href="https://phys.libretexts.org/Bookshelves/Modern_Physics/Book%3A_Spiral_Modern_Physics_(D&#39;Alessandris)/6%3A_The_Schrodinger_Equation/6.4%3A_Expectation_Values_Observables_and_Uncertainty">LibreTexts PHYSICS, 6.4: Expectation Values, Observables, and Uncertainty</a></li></ul><hr/><p class="math-container">\[ \begin{aligned}
\langle p^2 \rangle
Expand Down Expand Up @@ -377,5 +377,5 @@
1.0 1 9.8696043189632228 9.8696044010893580 0.0000008321117229% ✔
7.0 1 0.2014204963826796 0.2014204979814155 0.0000007937304979% ✔
Test Summary: | Pass Total Time
&lt;ψₙ|p²|ψₙ&gt; = ∫ψₙ*(-ℏ²d²/dx²)ψₙdx = π²ℏ²/L² | 4 4 0.4s
</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../HarmonicOscillator/">Harmonic Oscillator »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.0 on <span class="colophon-date" title="Wednesday 29 November 2023 21:33">Wednesday 29 November 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
&lt;ψₙ|p²|ψₙ&gt; = ∫ψₙ*(-ℏ²d²/dx²)ψₙdx = π²ℏ²/L² | 4 4 0.5s
</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../HarmonicOscillator/">Harmonic Oscillator »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.0 on <span class="colophon-date" title="Wednesday 29 November 2023 23:37">Wednesday 29 November 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
Loading

0 comments on commit ed98869

Please sign in to comment.