Add FDM.md

docs/make.jl

@@ -17,7 +17,8 @@ makedocs(;
     pages=[
         "Home" => "index.md",
         "Hamiltonian" => "Hamiltonian.md",
-        "Rayleigh–Ritz method" => "Rayleigh–Ritz.md",
+        "Rayleigh–Ritz Method" => "Rayleigh–Ritz.md",
+        "Finite Difference Method" => "FDM.md",
         "API reference" => "API.md",
     ],
 )

docs/src/FDM.md

@@ -0,0 +1,71 @@
+```@meta
+CurrentModule = TwoBody
+```
+
+# Finite Difference Method
+
+```@example example
+using TwoBody
+```
+
+```@example example
+H = Hamiltonian(
+  NonRelativisticKinetic(ℏ = 1 , m = 1),
+  CoulombPotential(coefficient = -1),
+)
+nothing # hide
+```
+
+```@example example
+FDM = FiniteDifferenceMethod(
+  Δr = 0.1,
+  rₘₐₓ = 50.0,
+  l = 0,
+  direction = :c,
+  solver = :LinearAlgebra,
+)
+nothing # hide
+```
+
+```@repl example
+solve(H, FDM)
+```
+
+```@example example
+# solve
+using TwoBody
+H = Hamiltonian(NonRelativisticKinetic(1,1), CoulombPotential(-1))
+FDM = TwoBody.FiniteDifferenceMethod()
+res = solve(H, FDM, info=0, nₘₐₓ=4)
+
+# benchmark
+import Antique
+HA = Antique.HydrogenAtom(Z=1, Eₕ=1.0, a₀=1.0, mₑ=1.0, ℏ=1.0)
+
+# plot
+using CairoMakie
+fig = Figure(
+  size = (840,600),
+  fontsize = 11.5,
+  backgroundcolor = :transparent
+)
+for n in 1:4
+  axis = Axis(
+    fig[div(n-1,2)+1,rem(n-1,2)+1],
+    xlabel = L"$r~/~a_0$",
+    ylabel = L"$4\pi r^2|\psi(r)|^2~ /~{a_0}^{-1}$",
+    xlabelsize = 16.5,
+    ylabelsize = 16.5,
+    limits=(
+      0, [5, 15, 30, 50][n],
+      0, [0.6, 0.2, 0.11, 0.07][n],
+    )
+  )
+  X = res.method.R
+  Y = 4π * X .^2 .* res.ψ[:,n] .^ 2
+  scatter!(axis, X, Y, label="TwoBody.jl", markersize=6)
+  lines!(axis, 0..50, r -> 4π * r^2 * abs(Antique.ψ(HA,r,0,0,n=n))^2, label="Antique.jl", color=:black)
+  axislegend(axis, "n = $n", position=:rt, framevisible=false)
+end
+fig
+```