Multi-dispatch version

Project.toml

@@ -1,7 +1,7 @@
 name = "Antique"
 uuid = "be6e5d0e-34a5-4c8f-af83-e1b5389203d8"
 authors = ["Shuhei Ohno"]
-version = "0.1.2"
+version = "0.2.0"
 
 [deps]
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"

README.md

@@ -16,7 +16,7 @@ using Pkg; Pkg.add("Antique")
 
 ## Usage & Examples
 
-Install Antique.jl for the first use and run `using Antique` before each use. The function `antique(model, parameters...)` returns a module that has `E`, `ψ`, `V` and some other functions. Here are examples in hydrogen-like atom. The analytical notation of energy (eigen value of the Hamiltonian) is written as
+Install Antique.jl for the first use and run `using Antique` before each use. The energy `E()`, wavefunction `ψ()`, potential `V()` and some other functions are suppoted. Here are examples in hydrogen-like atom. The analytical notation of energy (eigen value of the Hamiltonian) is written as
 
 ```math
 E_n = -\frac{Z^2}{2n^2} E_\mathrm{h}.
@@ -26,28 +26,28 @@ Hydrogen atom has symbol $\mathrm{H}$ and atomic number 1 ($Z=1$). Therefore the
 
 ```julia
 using Antique
-H = antique(:HydrogenAtom, Z=1)
-H.E(n=1)
+H = HydrogenAtom(Z=1)
+E(H)
 # output> -0.5
 ```
 
 Helium cation has symbol $\mathrm{He}^+$ and atomic number 2 ($Z=2$). Therefore the ground state ($n=1$) energy is $-2 E_\mathrm{h}$.
 
 ```julia
 using Antique
-He⁺ = antique(:HydrogenAtom, Z=2)
-He⁺.E(n=1)
+He⁺ = HydrogenAtom(Z=2)
+E(He⁺)
 # output> -2.0
 ```
 
 There are more examples on each model page.
 
 ## Supported Models
 
-- [Infinite Potential Well](https://ohno.github.io/Antique.jl/dev/InfinitePotentialWell/) `:InfinitePotentialWell`
-- [Harmonic Oscillator](https://ohno.github.io/Antique.jl/dev/HarmonicOscillator/) `:HarmonicOscillator`
-- [Morse Potential](https://ohno.github.io/Antique.jl/dev/MorsePotential/) `:MorsePotential`
-- [Hydrogen Atom](https://ohno.github.io/Antique.jl/dev/HydrogenAtom/) `:HydrogenAtom`
+- [Infinite Potential Well](https://ohno.github.io/Antique.jl/dev/InfinitePotentialWell/) `InfinitePotentialWell`
+- [Harmonic Oscillator](https://ohno.github.io/Antique.jl/dev/HarmonicOscillator/) `HarmonicOscillator`
+- [Morse Potential](https://ohno.github.io/Antique.jl/dev/MorsePotential/) `MorsePotential`
+- [Hydrogen Atom](https://ohno.github.io/Antique.jl/dev/HydrogenAtom/) `HydrogenAtom`
 
 ## Future Works
 

developer/dev.ipynb

@@ -10,21 +10,66 @@
  "name": "stderr",
  "output_type": "stream",
  "text": [
- "\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m new project at `C:\\Users\\user\\Desktop\\GitHub\\Antique.jl\\developer`\n"
+ "\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m project at `C:\\Users\\user\\Desktop\\Antique.jl`\n",
+ "\u001b[36m\u001b[1m[ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mPrecompiling Antique [be6e5d0e-34a5-4c8f-af83-e1b5389203d8]\n"
  ]
  }
  ],
  "source": [
- "include(\"revice.jl\")"
+ "# run `include(\"./developer/revice.jl\")`\n",
+ "using Pkg\n",
+ "Pkg.instantiate()\n",
+ "# Pkg.add(\"Revise\")\n",
+ "using Revise\n",
+ "Pkg.activate(\"../\")\n",
+ "using Antique"
  ]
  },
  {
  "cell_type": "code",
- "execution_count": null,
- "id": "97a634d3",
+ "execution_count": 2,
+ "id": "526ca10f",
  "metadata": {},
- "outputs": [],
- "source": []
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "-0.5"
+ ]
+ },
+ "execution_count": 2,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "using Antique\n",
+ "H = HydrogenAtom(Z=1)\n",
+ "E(H)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "4e1782eb",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "-2.0"
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "using Antique\n",
+ "He⁺ = HydrogenAtom(Z=2)\n",
+ "E(He⁺)"
+ ]
  }
  ],
  "metadata": {

docs/jmd2md.jl

@@ -1,7 +1,7 @@
 using Antique
 using Weave
 
-for file in Antique.models # [:InfinitePotentialWell]
+for file in Antique.models # [:InfinitePotentialWell :HarmonicOscillator :MorsePotential :HydrogenAtom]
  weave("./src/jmd/$file.jmd", doctype="github", out_path="./src/", fig_path="./assets/fig/")
  text = Antique.load("./src/$file.md")
  # remove ``` after include(...s)

docs/src/HarmonicOscillator.md

@@ -25,7 +25,7 @@ The harmonic oscillator is the most frequently used model in quantum physics.
 ```
 
 #### Potential
-`V(x; k=k, m=m, ω=sqrt(k/m))`
+`V(model::HarmonicOscillator; x)`
 ```math
  V(x)
  = \frac{1}{2} k x^2
@@ -34,19 +34,19 @@ The harmonic oscillator is the most frequently used model in quantum physics.
 ```
 
 #### Eigen Values
-`E(n; k, m, ω=sqrt(k/m), ℏ=ℏ)`
+`E(model::HarmonicOscillator; n=0)`
 ```math
  E_n = \hbar \omega \left( n + \frac{1}{2} \right)
 ```
 
 #### Eigen Functions
-`ψ(n, x; k=k, m=m, ω=sqrt(k/m), ℏ=ℏ)`
+`ψ(model::HarmonicOscillator, x; n=0)`
 ```math
  \psi_n(x) = A_n H_n(\xi) \exp{\left( -\frac{\xi^2}{2} \right)}
 ```
 
 #### Hermite Polynomials
-`H(x; n=0)`
+`H(model::HarmonicOscillator, x; n=0)`
 
 Rodrigues' formula & closed-form:
 ```math
@@ -88,11 +88,11 @@ Examples:
 
 ## Usage & Examples
 
-[Install Antique.jl](@ref Install) for the first use and run `using Antique` before each use. The function `antique(model, parameters...)` returns a module that has `E()`, `ψ(x)`, `V(x)` and some other functions. In this system, the model name is specified by `:HarmonicOscillator` and several parameters `k`, `m` and `ℏ` are set as optional arguments.
+[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 `HarmonicOscillator` and several parameters `k`, `m` and `ℏ` are set as optional arguments.
 
 ```julia
 using Antique
-HO = antique(:HarmonicOscillator, k=1.0, m=1.0, ℏ=1.0)
+HO = HarmonicOscillator(k=1.0, m=1.0, ℏ=1.0)
 ```
 
 
@@ -116,10 +116,10 @@ julia> HO.ℏ
 Eigen values:
 
 ```julia
-julia> HO.E(n=0)
+julia> E(HO, n=0)
 0.5
 
-julia> HO.E(n=1)
+julia> E(HO, n=1)
 1.5
 ```
 
@@ -129,7 +129,7 @@ Potential energy curve:
 
 ```julia
 using Plots
-plot(-5:0.1:5, x -> HO.V(x), lw=2, label="", xlabel="x", ylabel="V(x)")
+plot(-5:0.1:5, x -> V(HO, x), lw=2, label="", xlabel="x", ylabel="V(x)")
 ```
 
 ![](./assets/fig//HarmonicOscillator_4_1.png)
@@ -141,11 +141,11 @@ Wave functions:
 ```julia
 using Plots
 plot(xlim=(-5,5), xlabel="x", ylabel="ψ(x)")
-plot!(x -> HO.ψ(x, n=0), label="n=0", lw=2)
-plot!(x -> HO.ψ(x, n=1), label="n=1", lw=2)
-plot!(x -> HO.ψ(x, n=2), label="n=2", lw=2)
-plot!(x -> HO.ψ(x, n=3), label="n=3", lw=2)
-plot!(x -> HO.ψ(x, n=4), label="n=4", lw=2)
+plot!(x -> ψ(HO, x, n=0), label="n=0", lw=2)
+plot!(x -> ψ(HO, x, n=1), label="n=1", lw=2)
+plot!(x -> ψ(HO, x, n=2), label="n=2", lw=2)
+plot!(x -> ψ(HO, x, n=3), label="n=3", lw=2)
+plot!(x -> ψ(HO, x, n=4), label="n=4", lw=2)
 ```
 
 ![](./assets/fig//HarmonicOscillator_5_1.png)
@@ -159,13 +159,13 @@ using Plots
 plot(xlim=(-5.5,5.5), ylim=(-0.2,5.4), xlabel="\$x\$", ylabel="\$V(x),~E_n,~\\psi_n(x)\\times0.5+E_n\$", size=(480,400), dpi=300)
 for n in 0:4
  # energy
- hline!([HO.E(n=n)], lc=:black, ls=:dash, label="")
- plot!([-sqrt(2*HO.k*HO.E(n=n)),sqrt(2*HO.k*HO.E(n=n))], fill(HO.E(n=n),2), lc=:black, lw=2, label="")
+ hline!([E(HO, n=n)], lc=:black, ls=:dash, label="")
+ plot!([-sqrt(2*HO.k*E(HO, n=n)),sqrt(2*HO.k*E(HO, n=n))], fill(E(HO, n=n),2), lc=:black, lw=2, label="")
  # wave function
- plot!(x -> HO.E(n=n) + 0.5*HO.ψ(x,n=n), lc=n+1, lw=2, label="")
+ plot!(x -> E(HO, n=n) + 0.5*ψ(HO, x,n=n), lc=n+1, lw=2, label="")
 end
 # potential
-plot!(x -> HO.V(x), lc=:black, lw=2, label="")
+plot!(x -> V(HO, x), lc=:black, lw=2, label="")
 ```
 
 ![](./assets/fig//HarmonicOscillator_6_1.png)

docs/src/HydrogenAtom.md

@@ -22,7 +22,7 @@ The hydrogen atom is the simplest 2-body Coulomb system.
 Where, $\mu=\left(\frac{1}{m_\mathrm{e}}+\frac{1}{m_\mathrm{p}}\right)^{-1}$ is the reduced mass of electron $\mathrm{e}$ and proton $\mathrm{p}$. $\mu = m_\mathrm{e}$ holds in the limit $m_\mathrm{p}\rightarrow\infty$. 
 
 #### Potential
-`V(r; Z=Z, a₀=a₀)`
+`V(model::HydrogenAtom, r)`
 ```math
  \begin{aligned}
  V(r)
@@ -33,27 +33,27 @@ Where, $\mu=\left(\frac{1}{m_\mathrm{e}}+\frac{1}{m_\mathrm{p}}\right)^{-1}$ is
 ```
 
 #### Eigen Values
-`E(; n=1, Z=Z, Eₕ=Eₕ)`
+`E(model::HydrogenAtom; n=1)`
 ```math
  E_n = -\frac{m_\mathrm{e} e^4 Z^2}{2n^2(4\pi\varepsilon_0)^2\hbar^2} = -\frac{Z^2}{2n^2} E_\mathrm{h}
 ```
 Where, ``E_\mathrm{h}`` is the Hartree energy, one of atomic unit. About atomic units, see section 3.9.2 of the [IUPAC GreenBook](https://iupac.org/what-we-do/books/greenbook/). In other units, ``E_\mathrm{h} = 27.211~386~245~988(53)~\mathrm{eV}`` from [here](https://physics.nist.gov/cgi-bin/cuu/Value?hrev).
 
 #### Eigen Functions
-`ψ(r, θ, φ; n=1, l=0, m=0, Z=Z, a₀=a₀)`
+`ψ(model::HydrogenAtom, r, θ, φ; n=1, l=0, m=0)`
 ```math
  \psi_{nlm}(\pmb{r}) = R_{nl}(r) Y_{lm}(\theta,\varphi)
 ```
 
 #### Radial Functions
-`R(r; n=1, l=0, Z=Z, a₀=a₀)`
+`R(model::HydrogenAtom, r; n=1, l=0)`
 ```math
  R_{nl}(r) = -\sqrt{\frac{(n-l-1)!}{2n(n+l)!} \left(\frac{2Z}{n a_0}\right)^3} \left(\frac{2Zr}{n a_0}\right)^l \exp \left(-\frac{Zr}{n a_0}\right) L_{n+l}^{2l+1} \left(\frac{2Zr}{n a_0}\right)
 ```
 Where, Laguerre polynomials are defined as ``L_n(x) = \frac{1}{n!} \mathrm{e}^x \frac{\mathrm{d}^n}{\mathrm{d}x ^n} \left( \mathrm{e}^{-x} x^n \right)``, and associated Laguerre polynomials are defined as ``L_n^{k}(x) = \frac{\mathrm{d}^k}{\mathrm{d}x^k} L_n(x)``. Note that, replace ``2n(n+l)!`` with ``2n[(n+l)!]^3`` if Laguerre polynomials are defined as ``L_n(x) = \mathrm{e}^x \frac{\mathrm{d}^n}{\mathrm{d}x ^n} \left( \mathrm{e}^{-x} x^n \right)``.
 
 #### Associated Laguerre Polynomials
-`L(x; n=0, k=0)`
+`L(model::HydrogenAtom, x; n=0, k=0)`
 
 Rodrigues' formula & closed-form:
 ```math
@@ -91,7 +91,7 @@ Examples:
 ```
 
 #### Spherical Harmonics
-`Y(θ, φ; l=0, m=0)`
+`Y(model::HydrogenAtom, θ, φ; l=0, m=0)`
 ```math
  Y_{lm}(\theta,\varphi) = (-1)^{\frac{|m|+m}{2}} \sqrt{\frac{2l+1}{4\pi} \frac{(l-|m|)!}{(l+|m|)!}} P_l^{|m|} (\cos\theta) \mathrm{e}^{im\varphi}
 ```
@@ -101,7 +101,7 @@ i^{|m|+m} \sqrt{\frac{(l-|m|)!}{(l+|m|)!}} P_l^{|m|} = (-1)^{\frac{|m|+m}{2}} \s
 ```
 
 #### Associated Legendre Polynomials
-`P(x; n=0, m=0)`
+`P(model::HydrogenAtom, x; n=0, m=0)`
 
 Rodrigues' formula & closed-form:
 ```math
@@ -151,11 +151,11 @@ Examples:
 
 ## Usage & Examples
 
-[Install Antique.jl](@ref Install) for the first use and run `using Antique` before each use. The function `antique(model, parameters...)` returns a module that has `E()`, `ψ(r)`, `V(r)` and some other functions. In this system, the model name is specified by `:HydrogenAtom` and several parameters `Z`, `Eₕ`, `mₑ`, `a₀` and `ℏ` are set as optional arguments.
+[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 `HydrogenAtom` and several parameters `Z`, `Eₕ`, `mₑ`, `a₀` and `ℏ` are set as optional arguments.
 
 ```julia
 using Antique
-H = antique(:HydrogenAtom, Z=1, Eₕ=1.0, a₀=1.0, mₑ=1.0, ℏ=1.0)
+H = HydrogenAtom(Z=1, Eₕ=1.0, a₀=1.0, mₑ=1.0, ℏ=1.0)
 ```
 
 
@@ -185,10 +185,10 @@ julia> H.ℏ
 Eigen values:
 
 ```julia
-julia> H.E(n=1)
+julia> E(H, n=1)
 -0.5
 
-julia> H.E(n=2)
+julia> E(H, n=2)
 -0.125
 ```
 
@@ -198,8 +198,8 @@ Wave length ($n=2\rightarrow1$, the first line of the Lyman series):
 
 ```julia
 Eₕ2nm⁻¹ = 2.1947463136320e-2 # https://physics.nist.gov/cgi-bin/cuu/CCValue?hrminv
-println("ΔE = ", H.E(n=2) - H.E(n=1), " Eₕ")
-println("λ = ", ((H.E(n=2)-H.E(n=1))*Eₕ2nm⁻¹)^-1, " nm")
+println("ΔE = ", E(H,n=2) - E(H,n=1), " Eₕ")
+println("λ = ", ((E(H,n=2)-E(H,n=1))*Eₕ2nm⁻¹)^-1, " nm")
 ```
 
 ```
@@ -226,7 +226,7 @@ ge = 2.00231930436256 # https://physics.nist.gov/cgi-bin/cuu/Value?gem
 gp = 5.5856946893 # https://physics.nist.gov/cgi-bin/cuu/Value?gp
 
 # calculation: https://doi.org/10.1119/1.12733
-δ = abs(H.ψ(0,0,0))^2
+δ = abs(ψ(H,0,0,0))^2
 ΔE = 2 / 3 * µ0 * µN * µB * gp * ge * δ * a0^(-3)
 println("1/π = ", 1/π)
 println("<δ(r)> = ", δ, " a₀⁻³")
@@ -254,7 +254,7 @@ Potential energy curve:
 ```julia
 using Plots
 plot(xlims=(0.0,15.0), ylims=(-0.6,0.05), xlabel="\$r~/~a_0\$", ylabel="\$V(r)/E_\\mathrm{h},~E_n/E_\\mathrm{h}\$", legend=:bottomright, size=(480,400))
-plot!(0.1:0.01:15, r -> H.V(r), lc=:black, lw=2, label="") # potential
+plot!(0.1:0.01:15, r -> V(H,r), lc=:black, lw=2, label="") # potential
 ```
 
 ![](./assets/fig//HydrogenAtom_6_1.png)
@@ -267,9 +267,9 @@ Potential energy curve, Energy levels:
 using Plots
 plot(xlims=(0.0,15.0), ylims=(-0.6,0.05), xlabel="\$r~/~a_0\$", ylabel="\$V(r)/E_\\mathrm{h}\$", legend=:bottomright, size=(480,400))
 for n in 0:10
- plot!(0.0:0.01:15, r -> H.E(n=n) > H.V(r) ? H.E(n=n) : NaN, lc=n, lw=1, label="") # energy level
+ plot!(0.0:0.01:15, r -> E(H,n=n) > V(H,r) ? E(H,n=n) : NaN, lc=n, lw=1, label="") # energy level
 end
-plot!(0.1:0.01:15, r -> H.V(r), lc=:black, lw=2, label="") # potential
+plot!(0.1:0.01:15, r -> V(H,r), lc=:black, lw=2, label="") # potential
 ```
 
 ![](./assets/fig//HydrogenAtom_7_1.png)
@@ -283,7 +283,7 @@ using Plots
 plot(xlabel="\$r~/~a_0\$", ylabel="\$r^2|R_{nl}(r)|^2~/~a_0^{-1}\$", ylims=(-0.01,0.55), xticks=0:1:20, size=(480,400), dpi=300)
 for n in 1:3
  for l in 0:n-1
- plot!(0:0.01:20, r->r^2*H.R(r,n=n,l=l)^2, lc=n, lw=2, ls=[:solid,:dash,:dot,:dashdot,:dashdotdot][l+1], label="\$n = $n, l=$l\$")
+ plot!(0:0.01:20, r->r^2*R(H,r,n=n,l=l)^2, lc=n, lw=2, ls=[:solid,:dash,:dot,:dashdot,:dashdotdot][l+1], label="\$n = $n, l=$l\$")
  end
 end
 plot!()