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Normalize wave function

This commit is contained in:
Nuwan Yapa 2024-07-17 15:37:30 -04:00
parent 5248fdafb3
commit 9e24943a2d
1 changed files with 12 additions and 5 deletions
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17
dirac.jl
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@ -24,10 +24,10 @@ function dirac!(du, u, (κ, p, E, Φ0, W0, B0, A0), r)
end end
"Solve the Dirac equation and return the wave function u(r)=[g(r), f(r)] where "Solve the Dirac equation and return the wave function u(r)=[g(r), f(r)] where
divs is the number of mesh divisions if the solution should be discretized as a 2×(1+divs) matrix (keep divs=0 to obtain an interpolating function), divs is the number of mesh divisions so solution would be returned as a 2×(1+divs) matrix,
refine determines whether to switch to high-precision mode and optimize the energy beforehand (assuming a bound state), refine determines whether to switch to high-precision mode and optimize the energy beforehand (assuming a bound state),
the other parameters are the same from dirac!(...)." the other parameters are the same from dirac!(...)."
function solveWf(κ, p, E, Φ0, W0, B0, A0, r_max, divs::Int=0, refine=true) function solveWf(κ, p, E, Φ0, W0, B0, A0, r_max, divs; refine=true, normalize=true)
if refine if refine
dtype = BigFloat dtype = BigFloat
algo = Feagin12() algo = Feagin12()
@ -40,8 +40,15 @@ function solveWf(κ, p, E, Φ0, W0, B0, A0, r_max, divs::Int=0, refine=true)
end end
prob = ODEProblem(dirac!, convert.(dtype, [0, 1]), (0, r_max)) prob = ODEProblem(dirac!, convert.(dtype, [0, 1]), (0, r_max))
sol = solve(prob, algo, p=(κ, p, E, Φ0, W0, B0, A0), saveat=(divs == 0 ? [] : r_max/divs)) sol = solve(prob, algo, p=(κ, p, E, Φ0, W0, B0, A0), saveat=r_max/divs)
return divs == 0 ? sol : hcat(sol.u...) wf = hcat(sol.u...)
if normalize
norm = sum(wf .* wf) * r_max / divs # integration by Reimann sum
wf = wf ./ sqrt(norm)
end
return wf
end end
"Solve the Dirac equation and return g(r=r_max) where "Solve the Dirac equation and return g(r=r_max) where
@ -112,7 +119,7 @@ function calculateNucleonDensity(N, p, Φ0, W0, B0, A0, r_max, divs, E_min=0, E_
ρ_v = zeros(divs + 1) ρ_v = zeros(divs + 1)
for (κ, E, occ) in zip(κs, Es, occs) for (κ, E, occ) in zip(κs, Es, occs)
wf = solveWf(κ, p, E, Φ0, W0, B0, A0, r_max, divs) # TODO: Needs to be normalized wf = solveWf(κ, p, E, Φ0, W0, B0, A0, r_max, divs; refine=true, normalize=true)
wf2 = wf .* wf wf2 = wf .* wf
ρ = (occ / (4 * pi)) * (wf2 ./ r2s) # 2j+1 factor is accounted in the occupancy number ρ = (occ / (4 * pi)) * (wf2 ./ r2s) # 2j+1 factor is accounted in the occupancy number