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14 changes: 7 additions & 7 deletions docs/src/FDM.md
Original file line number Diff line number Diff line change
Expand Up @@ -57,7 +57,7 @@ FDM = FiniteDifferenceMethod(
nothing # hide
```

Solve the eigenvalue problem. You should find reasonable approximations to [the exact eigenvalues](https://ohno.github.io/Antique.jl/stable/HydrogenAtom/#Antique.E-Tuple{HydrogenAtom}-HydrogenAtom):
Solve the eigenvalue problem. You should find reasonable approximations to [the exact eigenvalues](https://ohno.github.io/Antique.jl/stable/HydrogenAtom/#Eigenvalues):
```math
\begin{aligned}
E_{n=1} &= -0.5,\\
Expand Down Expand Up @@ -85,7 +85,7 @@ 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, =1.0)
HA = Antique.HydrogenAtom(Z=1, E_h=1.0, a_0=1.0, m_e=1.0, hbar=1.0)

# energy
using Printf
Expand All @@ -94,7 +94,7 @@ println("------------------------------")
println(" n numerical analytical")
println("------------------------------")
for n in 1:4
@printf("%2d %+.9f %+.9f\n", n, res.E[n], Antique.E(HA,n=n))
@printf("%2d %+.9f %+.9f\n", n, res.E[n], Antique.energy(HA,n=n))
end

# wave function
Expand All @@ -119,7 +119,7 @@ for n in 1:4
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)
lines!(axis, 0..50, r -> 4π * r^2 * abs(Antique.wavefunction(HA,r,0,0,n=n))^2, label="Antique.jl", color=:black)
axislegend(axis, "n = $n", position=:rt, framevisible=false)
end
save("assets/FDM_HA.svg", fig) # hide
Expand All @@ -140,7 +140,7 @@ res = solve(H, FDM, info=0, nₘₐₓ=4)

# benchmark
import Antique
SO = Antique.SphericalOscillator(k=1.0, μ=1.0, =1.0)
SO = Antique.SphericalOscillator(k=1.0, mu=1.0, hbar=1.0)

# energy
using Printf
Expand All @@ -149,7 +149,7 @@ println("------------------------------")
println(" n numerical analytical")
println("------------------------------")
for n in 1:4
@printf("%2d %+.9f %+.9f\n", n-1, res.E[n], Antique.E(SO,n=n-1))
@printf("%2d %+.9f %+.9f\n", n-1, res.E[n], Antique.energy(SO,n=n-1))
end

# wave function
Expand All @@ -174,7 +174,7 @@ for n in 1:4
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(SO,r,0,0,n=n-1))^2, label="Antique.jl", color=:black)
lines!(axis, 0..50, r -> 4π * r^2 * abs(Antique.wavefunction(SO,r,0,0,n=n-1))^2, label="Antique.jl", color=:black)
axislegend(axis, "n = $(n-1)", position=:rt, framevisible=false)
end
fig
Expand Down
12 changes: 6 additions & 6 deletions docs/src/Rayleigh-Ritz.md
Original file line number Diff line number Diff line change
Expand Up @@ -84,7 +84,7 @@ res = solve(H, BS)

# benchmark
import Antique
HA = Antique.HydrogenAtom(Z=1, Eₕ=1.0, a₀=1.0, mₑ=1.0, =1.0)
HA = Antique.HydrogenAtom(Z=1, E_h=1.0, a_0=1.0, m_e=1.0, hbar=1.0)

# energy
using Printf
Expand All @@ -93,7 +93,7 @@ println("------------------------------")
println(" n numerical analytical")
println("------------------------------")
for n in 1:4
@printf("%2d %+.9f %+.9f\n", n, res.E[n], Antique.E(HA,n=n))
@printf("%2d %+.9f %+.9f\n", n, res.E[n], Antique.energy(HA,n=n))
end

# wave function
Expand All @@ -116,7 +116,7 @@ for n in 1:4
)
)
lines!(axis, 0..50, r -> 4π * r^2 * abs(TwoBody.ψ(res,r,n=n))^2, label="TwoBody.jl")
lines!(axis, 0..50, r -> 4π * r^2 * abs(Antique.ψ(HA,r,0,0,n=n))^2, label="Antique.jl", color=:black, linestyle=:dash)
lines!(axis, 0..50, r -> 4π * r^2 * abs(Antique.wavefunction(HA,r,0,0,n=n))^2, label="Antique.jl", color=:black, linestyle=:dash)
axislegend(axis, "n = $n", position=:rt, framevisible=false)
end
fig
Expand All @@ -138,7 +138,7 @@ res = solve(H, BS)

# benchmark
import Antique
SO = Antique.SphericalOscillator(k=1.0, μ=1.0, =1.0)
SO = Antique.SphericalOscillator(k=1.0, mu=1.0, hbar=1.0)

# energy
using Printf
Expand All @@ -147,7 +147,7 @@ println("------------------------------")
println(" n numerical analytical")
println("------------------------------")
for n in 1:4
@printf("%2d %+.9f %+.9f\n", n-1, res.E[n], Antique.E(SO,n=n-1))
@printf("%2d %+.9f %+.9f\n", n-1, res.E[n], Antique.energy(SO,n=n-1))
end

# wave function
Expand All @@ -170,7 +170,7 @@ for n in 1:4
)
)
lines!(axis, 0..50, r -> 4π * r^2 * abs(TwoBody.ψ(res,r,n=n))^2, label="TwoBody.jl")
lines!(axis, 0..50, r -> 4π * r^2 * abs(Antique.ψ(SO,r,0,0,n=n-1))^2, label="Antique.jl", color=:black, linestyle=:dash)
lines!(axis, 0..50, r -> 4π * r^2 * abs(Antique.wavefunction(SO,r,0,0,n=n-1))^2, label="Antique.jl", color=:black, linestyle=:dash)
axislegend(axis, "n = $(n-1)", position=:rt, framevisible=false)
end
fig
Expand Down
4 changes: 2 additions & 2 deletions docs/src/index.md
Original file line number Diff line number Diff line change
Expand Up @@ -74,14 +74,14 @@ res = solve(H, BS)

# benchmark
import Antique
HA = Antique.HydrogenAtom(Z=1, Eₕ=1.0, a₀=1.0, mₑ=1.0, =1.0)
HA = Antique.HydrogenAtom(Z=1, E_h=1.0, a_0=1.0, m_e=1.0, hbar=1.0)

# plot
using CairoMakie
fig = Figure(size=(420,300), fontsize=11, backgroundcolor=:transparent)
axis = Axis(fig[1,1], xlabel=L"$r / a_0$", ylabel=L"$\psi(r) / a_0^{-3/2}$", ylabelsize=16.5, xlabelsize=16.5, limits=(0,4,0,1.1/sqrt(π)))
lines!(axis, 0..5, r -> abs(TwoBody.ψ(res,r)), label="TwoBody.jl")
lines!(axis, 0..5, r -> abs(Antique.ψ(HA,r,0,0)), linestyle=:dash, color=:black, label="Antique.jl")
lines!(axis, 0..5, r -> abs(Antique.wavefunction(HA,r,0,0)), linestyle=:dash, color=:black, label="Antique.jl")
axislegend(axis, position=:rt, framevisible=false)
fig
```
Expand Down
6 changes: 3 additions & 3 deletions test/FDM.jl
Original file line number Diff line number Diff line change
Expand Up @@ -38,13 +38,13 @@
end

# comparison with Antique.jl
HA = Antique.HydrogenAtom(Z=1, mₑ=1.0, a₀=1.0, Eₕ=1.0, =1.0)
HA = Antique.HydrogenAtom(Z=1, m_e=1.0, a_0=1.0, E_h=1.0, hbar=1.0)

println("Energy")
println(" i\tnumerical \tanalytical")
for i in 1:res.nₘₐₓ
numerical = res.E[i]
analytical = Antique.E(HA, n=i)
analytical = Antique.energy(HA, n=i)
error = iszero(analytical) ? abs(numerical-analytical) : abs((numerical-analytical)/analytical)
acceptance = error < 1e-2
@printf("%3d\t%.9f\t%.9f\t%s\n", i, numerical, analytical, acceptance ? "✔" : "✗")
Expand All @@ -58,7 +58,7 @@
for i in keys(res.method.R[begin:min(10,length(res.method.R))])
r = res.method.R[i]
numerical = abs(res.ψ[i,n])
analytical = abs(Antique.ψ(HA, r, 0, 0, n=n))
analytical = abs(Antique.wavefunction(HA, r, 0, 0, n=n))
error = iszero(analytical) ? abs(numerical-analytical) : abs((numerical-analytical)/analytical)
acceptance = error < 5e-2
@printf("%3d\t%.1f\t%.9f\t%.9f\t%s\n", i, r, numerical, analytical, acceptance ? "✔" : "✗")
Expand Down
4 changes: 2 additions & 2 deletions test/Rayleigh-Ritz.jl
Original file line number Diff line number Diff line change
Expand Up @@ -58,13 +58,13 @@
@test acceptance

# comparison with Antique.jl
HA = Antique.HydrogenAtom(Z=1, mₑ=1.0, a₀=1.0, Eₕ=1.0, =1.0)
HA = Antique.HydrogenAtom(Z=1, m_e=1.0, a_0=1.0, E_h=1.0, hbar=1.0)

println("ψ(r)")
println(" r\tnumerical \tanalytical")
for r in 0.2:0.1:2.0
numerical = abs(TwoBody.ψ(res, r, n=1))
analytical = abs(Antique.ψ(HA, r, 0, 0))
analytical = abs(Antique.wavefunction(HA, r, 0, 0))
error = iszero(analytical) ? abs(numerical-analytical) : abs((numerical-analytical)/analytical)
acceptance = error < 1e-2
@printf("%.1f\t%.9f\t%.9f\t%s\n", r, numerical, analytical, acceptance ? "✔" : "✗")
Expand Down
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