update DeltaPotential

ohno · Feb 8, 2024 · 7f62365 · 7f62365
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diff --git a/docs/make.jl b/docs/make.jl
@@ -24,6 +24,7 @@ makedocs(;
     "Harmonic Oscillator"     => "HarmonicOscillator.md"   ,
     "Morse Potential"         => "MorsePotential.md"       ,
     "Hydrogen Atom"           => "HydrogenAtom.md"         ,
+    "Delta Potential"         => "DeltaPotential.md"       ,
   ],
 )
 

diff --git a/docs/src/DeltaPotential.md b/docs/src/DeltaPotential.md
@@ -2,7 +2,6 @@
 CurrentModule = Antique
 ```
 
-
 # Delta Potential
 
 The Delta potential is one the simplest models for quantum mechanical system in 1D.
@@ -19,7 +18,7 @@ It always has one bound state and its wave function has a cusp at the origin.
 
 #### Hamiltonian
 ```math
-  \hat{H} = \frac{\hbar^2}{2m} \frac{\mathrm{d}^2}{\mathrm{d}x ^2} + V(x)
+  \hat{H} = - \frac{\hbar^2}{2m} \frac{\mathrm{d}^2}{\mathrm{d}x ^2} + V(x)
 ```
 
 #### Potential
@@ -40,11 +39,97 @@ It always has one bound state and its wave function has a cusp at the origin.
    \psi(x) = \frac{\sqrt{m\alpha}}{\hbar} \mathrm{e}^{-m\alpha |x|/\hbar^2}
 ```
 
+## Usage & Examples
+
+[Install Antique.jl](@ref Install) for the first use and run `using Antique` before each use. The energy `E()`, wavefunction `ψ()`, potential `V()` and some other functions are suppoted. In this system, the model is generated by `DeltaPotential` and several parameters `α`, `m` and `ℏ` are set as optional arguments.
+
+```julia
+using Antique
+DP = DeltaPotential(α=1.0, m=1.0, ℏ=1.0)
+```
+
+
+
+
+Parameters:
+
+```julia
+julia> DP.α
+1.0
+
+julia> DP.m
+1.0
+
+julia> DP.ℏ
+1.0
+```
+
+
+
+Eigen values:
+
+```julia
+julia> E(DP)
+-0.5
+```
+
+
+
+Wave functions:
+
+```julia
+DP = DeltaPotential(α=0.1, m=0.5, ℏ=0.1)
+x = LinRange(-2,2,500);
+
+using Plots
+plot(x, x->ψ(DP,x), linewidth=3)
+plot!(xlim=[-2,2], ylim=[0,2.5], legend=false)
+plot!(xlabel="x", ylabel="ψ(x)", title="Delta Potential")
+```
+
+![](./assets/fig//DeltaPotential_4_1.png)
+
+
+
 ## Testing
 
 Unit testing and Integration testing were done using numerical integration ([QuadGK.jl](https://juliamath.github.io/QuadGK.jl/stable/)). The test script is [here](https://github.com/ohno/Antique.jl/blob/main/test/DeltaPotential.jl).
 
-Error: UndefVarError: `Antique` not defined
+#### Normalization of $\psi(x)$
+
+```math
+\int_{-\infty}^{\infty} \psi^\ast(x) \psi(x) ~\mathrm{d}x = 1
 ```
 
+```
+  α |   m |   ℏ |        analytical |         numerical 
+--- | --- | --- | ----------------- | ----------------- 
+0.1 | 0.1 | 0.1 |    1.000000000000 |    1.000000000000 ✔
+0.1 | 0.1 | 1.0 |    1.000000000000 |    1.000000000000 ✔
+0.1 | 0.1 | 7.0 |    1.000000000000 |    1.000004676239 ✔
+0.1 | 1.0 | 0.1 |    1.000000000000 |    1.000000000000 ✔
+0.1 | 1.0 | 1.0 |    1.000000000000 |    1.000000000000 ✔
+0.1 | 1.0 | 7.0 |    1.000000000000 |    0.999999999999 ✔
+0.1 | 7.0 | 0.1 |    1.000000000000 |    1.000000000000 ✔
+0.1 | 7.0 | 1.0 |    1.000000000000 |    1.000000000000 ✔
+0.1 | 7.0 | 7.0 |    1.000000000000 |    1.000000000000 ✔
+1.0 | 0.1 | 0.1 |    1.000000000000 |    1.000000000000 ✔
+1.0 | 0.1 | 1.0 |    1.000000000000 |    1.000000000000 ✔
+1.0 | 0.1 | 7.0 |    1.000000000000 |    0.999999999999 ✔
+1.0 | 1.0 | 0.1 |    1.000000000000 |    1.000000000000 ✔
+1.0 | 1.0 | 1.0 |    1.000000000000 |    1.000000000000 ✔
+1.0 | 1.0 | 7.0 |    1.000000000000 |    1.000000000000 ✔
+1.0 | 7.0 | 0.1 |    1.000000000000 |    1.000000000000 ✔
+1.0 | 7.0 | 1.0 |    1.000000000000 |    1.000000000000 ✔
+1.0 | 7.0 | 7.0 |    1.000000000000 |    1.000000000000 ✔
+7.0 | 0.1 | 0.1 |    1.000000000000 |    1.000000000000 ✔
+7.0 | 0.1 | 1.0 |    1.000000000000 |    1.000000000000 ✔
+7.0 | 0.1 | 7.0 |    1.000000000000 |    1.000000000000 ✔
+7.0 | 1.0 | 0.1 |    1.000000000000 |    1.000000000000 ✔
+7.0 | 1.0 | 1.0 |    1.000000000000 |    1.000000000000 ✔
+7.0 | 1.0 | 7.0 |    1.000000000000 |    1.000000000000 ✔
+7.0 | 7.0 | 0.1 |    1.000000000000 |    1.000000000000 ✔
+7.0 | 7.0 | 1.0 |    1.000000000000 |    1.000000000000 ✔
+7.0 | 7.0 | 7.0 |    1.000000000000 |    1.000000000000 ✔
 
+```
diff --git a/docs/src/InfinitePotentialWell.md b/docs/src/InfinitePotentialWell.md
@@ -17,7 +17,7 @@ The infinite potential well (particle in a box) is the simplest model for quantu
 
 #### Hamiltonian
 ```math
-  \hat{H} = \frac{\hbar^2}{2m} \frac{\mathrm{d}^2}{\mathrm{d}x ^2} + V(x)
+  \hat{H} = - \frac{\hbar^2}{2m} \frac{\mathrm{d}^2}{\mathrm{d}x ^2} + V(x)
 ```
 
 #### Potential

diff --git a/docs/src/assets/fig/DeltaPotential_4_1.png b/docs/src/assets/fig/DeltaPotential_4_1.png
diff --git a/docs/src/jmd/DeltaPotential.jmd b/docs/src/jmd/DeltaPotential.jmd
@@ -2,7 +2,6 @@
 CurrentModule = Antique
 ```
 
-
 # Delta Potential
 
 The Delta potential is one the simplest models for quantum mechanical system in 1D.
@@ -19,7 +18,7 @@ It always has one bound state and its wave function has a cusp at the origin.
 
 #### Hamiltonian
 ```math
-  \hat{H} = \frac{\hbar^2}{2m} \frac{\mathrm{d}^2}{\mathrm{d}x ^2} + V(x)
+  \hat{H} = - \frac{\hbar^2}{2m} \frac{\mathrm{d}^2}{\mathrm{d}x ^2} + V(x)
 ```
 
 #### Potential
@@ -40,6 +39,41 @@ It always has one bound state and its wave function has a cusp at the origin.
    \psi(x) = \frac{\sqrt{m\alpha}}{\hbar} \mathrm{e}^{-m\alpha |x|/\hbar^2}
 ```
 
+## Usage & Examples
+
+[Install Antique.jl](@ref Install) for the first use and run `using Antique` before each use. The energy `E()`, wavefunction `ψ()`, potential `V()` and some other functions are suppoted. In this system, the model is generated by `DeltaPotential` and several parameters `α`, `m` and `ℏ` are set as optional arguments.
+
+```julia; cache = :all; results = "hidden"
+using Antique
+DP = DeltaPotential(α=1.0, m=1.0, ℏ=1.0)
+```
+
+Parameters:
+
+```julia; term = true
+DP.α
+DP.m
+DP.ℏ
+```
+
+Eigen values:
+
+```julia; term = true
+E(DP)
+```
+
+Wave functions:
+
+```julia
+DP = DeltaPotential(α=0.1, m=0.5, ℏ=0.1)
+x = LinRange(-2,2,500);
+
+using Plots
+plot(x, x->ψ(DP,x), linewidth=3)
+plot!(xlim=[-2,2], ylim=[0,2.5], legend=false)
+plot!(xlabel="x", ylabel="ψ(x)", title="Delta Potential")
+```
+
 ## Testing
 
 Unit testing and Integration testing were done using numerical integration ([QuadGK.jl](https://juliamath.github.io/QuadGK.jl/stable/)). The test script is [here](https://github.com/ohno/Antique.jl/blob/main/test/DeltaPotential.jl).

diff --git a/docs/src/jmd/InfinitePotentialWell.jmd b/docs/src/jmd/InfinitePotentialWell.jmd
@@ -17,7 +17,7 @@ The infinite potential well (particle in a box) is the simplest model for quantu
 
 #### Hamiltonian
 ```math
-  \hat{H} = \frac{\hbar^2}{2m} \frac{\mathrm{d}^2}{\mathrm{d}x ^2} + V(x)
+  \hat{H} = - \frac{\hbar^2}{2m} \frac{\mathrm{d}^2}{\mathrm{d}x ^2} + V(x)
 ```
 
 #### Potential

diff --git a/test/DeltaPotential.jl b/test/DeltaPotential.jl
@@ -1,34 +1,31 @@
-DP = DeltaPotential(α=1.0,m=1.0, ℏ=1.0)
+DP = DeltaPotential(α=1.0, m=1.0, ℏ=1.0)
 
 # <ψᵢ|ψⱼ> = ∫ψ*ψdx = δᵢⱼ
 
 println(raw"""
-#### Normalization & Orthogonality of $\psi(x)$
+#### Normalization of $\psi(x)$
 
 ```math
-\int_{-Inf}^{Inf} \psi^\ast(x) \psi(x) ~\mathrm{d}x = 1
+\int_{-\infty}^{\infty} \psi^\ast(x) \psi(x) ~\mathrm{d}x = 1
 ```
 
 ```""")
 
 @testset "<ψ|ψ> = ∫ψ*ψdx = 1" begin
-  println("        analytical |         numerical ")
-  println(" ----------------- | ----------------- ")
-  # for L in [0.1, 0.5, 1.0, 7.0]
-  # for m in [0.1, 0.5, 1.0, 7.0]
-  # for ℏ in [0.1, 0.5, 1.0, 7.0]
-  #  for i in 1:10
-  #  for j in 1:10
+  println("  α |   m |   ℏ |        analytical |         numerical ")
+  println("--- | --- | --- | ----------------- | ----------------- ")
+  for α in [0.1, 1.0, 7.0]
+  for m in [0.1, 1.0, 7.0]
+  for ℏ in [0.1, 1.0, 7.0]
+    DP = DeltaPotential(α=α, m=m, ℏ=ℏ)
     analytical = 1
-    numerical  = quadgk(x -> conj(ψ(DP, x)) * ψ(DP, x), -Inf, Inf, maxevals=10^3)[1]
+    numerical  = quadgk(x -> conj(ψ(DP, x)) * ψ(DP, x), -Inf, Inf, maxevals=10^3, order=10)[1]
     acceptance = iszero(analytical) ? isapprox(analytical, numerical, atol=1e-5) : isapprox(analytical, numerical, rtol=1e-5)
     @test acceptance
-    @printf("%17.12f | %17.12f %s\n", analytical, numerical, acceptance ? "✔" : "✗")
-  #   end
-  #   end
-  # end
-  # end
-  # end
+    @printf("%.1f | %.1f | %.1f | %17.12f | %17.12f %s\n", α, m, ℏ, analytical, numerical, acceptance ? "✔" : "✗")
+  end
+  end
+  end
 end
 
 println("""```

diff --git a/test/result/DeltaPotential.log b/test/result/DeltaPotential.log
@@ -1,13 +1,39 @@
-#### Normalization & Orthogonality of $\psi(x)$
+#### Normalization of $\psi(x)$
 
 ```math
-\int_{-Inf}^{Inf} \psi^\ast(x) \psi(x) ~\mathrm{d}x = 1
+\int_{-\infty}^{\infty} \psi^\ast(x) \psi(x) ~\mathrm{d}x = 1
 ```
 
 ```
-        analytical |         numerical 
- ----------------- | ----------------- 
-   1.000000000000 |    1.000000000000 ✔
+  α |   m |   ℏ |        analytical |         numerical 
+--- | --- | --- | ----------------- | ----------------- 
+0.1 | 0.1 | 0.1 |    1.000000000000 |    1.000000000000 ✔
+0.1 | 0.1 | 1.0 |    1.000000000000 |    1.000000000000 ✔
+0.1 | 0.1 | 7.0 |    1.000000000000 |    1.000004676239 ✔
+0.1 | 1.0 | 0.1 |    1.000000000000 |    1.000000000000 ✔
+0.1 | 1.0 | 1.0 |    1.000000000000 |    1.000000000000 ✔
+0.1 | 1.0 | 7.0 |    1.000000000000 |    0.999999999999 ✔
+0.1 | 7.0 | 0.1 |    1.000000000000 |    1.000000000000 ✔
+0.1 | 7.0 | 1.0 |    1.000000000000 |    1.000000000000 ✔
+0.1 | 7.0 | 7.0 |    1.000000000000 |    1.000000000000 ✔
+1.0 | 0.1 | 0.1 |    1.000000000000 |    1.000000000000 ✔
+1.0 | 0.1 | 1.0 |    1.000000000000 |    1.000000000000 ✔
+1.0 | 0.1 | 7.0 |    1.000000000000 |    0.999999999999 ✔
+1.0 | 1.0 | 0.1 |    1.000000000000 |    1.000000000000 ✔
+1.0 | 1.0 | 1.0 |    1.000000000000 |    1.000000000000 ✔
+1.0 | 1.0 | 7.0 |    1.000000000000 |    1.000000000000 ✔
+1.0 | 7.0 | 0.1 |    1.000000000000 |    1.000000000000 ✔
+1.0 | 7.0 | 1.0 |    1.000000000000 |    1.000000000000 ✔
+1.0 | 7.0 | 7.0 |    1.000000000000 |    1.000000000000 ✔
+7.0 | 0.1 | 0.1 |    1.000000000000 |    1.000000000000 ✔
+7.0 | 0.1 | 1.0 |    1.000000000000 |    1.000000000000 ✔
+7.0 | 0.1 | 7.0 |    1.000000000000 |    1.000000000000 ✔
+7.0 | 1.0 | 0.1 |    1.000000000000 |    1.000000000000 ✔
+7.0 | 1.0 | 1.0 |    1.000000000000 |    1.000000000000 ✔
+7.0 | 1.0 | 7.0 |    1.000000000000 |    1.000000000000 ✔
+7.0 | 7.0 | 0.1 |    1.000000000000 |    1.000000000000 ✔
+7.0 | 7.0 | 1.0 |    1.000000000000 |    1.000000000000 ✔
+7.0 | 7.0 | 7.0 |    1.000000000000 |    1.000000000000 ✔
 ```
 
 
diff --git a/test/runtests.jl b/test/runtests.jl
@@ -10,7 +10,7 @@ using LaTeXStrings
 using SpecialFunctions
 
 @testset "Antique.jl" begin
-	for model in Antique.models
+	for model in [:DeltaPotential] # Antique.models
 		result = @capture_out begin
 			include("./$(model).jl")
 		end