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Fixed unstability of wave functions

This commit is contained in:
Nuwan Yapa 2024-07-16 18:29:35 -04:00
parent 6538c30fa8
commit f77e5dfed8
2 changed files with 18 additions and 11 deletions
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19
dirac.jl
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@ -26,18 +26,18 @@ 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 if the solution should be discretized as a 2×(1+divs) matrix (keep divs=0 to obtain an interpolating function),
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) function solveWf(κ, p, E, Φ0, W0, B0, A0, r_max, divs::Int=0; dtype=BigFloat, algo=Feagin12())
prob = ODEProblem(dirac!, [0, 1], (0, r_max)) prob = ODEProblem(dirac!, convert.(dtype, [0, 1]), (0, r_max))
sol = solve(prob, RK4(), 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=(divs == 0 ? [] : r_max/divs))
return divs == 0 ? sol : hcat(sol.u...) return divs == 0 ? sol : hcat(sol.u...)
end end
"Solve the Dirac equation and return g(r=r_max) where "Solve the Dirac equation and return g(r=r_max) where
r_max is the outer boundary in fm, r_max is the outer boundary in fm,
the other parameters are the same from dirac!(...)." the other parameters are the same from dirac!(...)."
function boundaryValue(κ, p, E, Φ0, W0, B0, A0, r_max) function boundaryValue(κ, p, E, Φ0, W0, B0, A0, r_max; dtype=Float64, algo=RK4())
prob = ODEProblem(dirac!, [0, 1], (0, r_max)) prob = ODEProblem(dirac!, convert.(dtype, [0, 1]), (0, r_max))
sol = solve(prob, RK4(), p=(κ, p, E, Φ0, W0, B0, A0), saveat=[r_max], save_idxs=[1]) sol = solve(prob, algo, p=(κ, p, E, Φ0, W0, B0, A0), saveat=[r_max], save_idxs=[1])
return sol[1, 1] return sol[1, 1]
end end
@ -48,6 +48,13 @@ function findEs(κ, p, Φ0, W0, B0, A0, r_max, E_min=0, E_max=(p ? M_p : M_n))
return find_zeros(f, (E_min, E_max)) return find_zeros(f, (E_min, E_max))
end end
"Find more precise bound energies for a given list of Es where
the other parameters are the same from dirac!(...)."
function refineEs(κ, p, Φ0, W0, B0, A0, r_max, Es)
f(E) = boundaryValue(κ, p, E, Φ0, W0, B0, A0, r_max; dtype=BigFloat, algo=Feagin12())
return [find_zero(f, E) for E in Es]
end
"Find all orbitals and return two lists containing κ values and corresponding energies for a single species where "Find all orbitals and return two lists containing κ values and corresponding energies for a single species where
the other parameters are defined above" the other parameters are defined above"
function findAllOrbitals(p, Φ0, W0, B0, A0, r_max, E_min=0, E_max=(p ? M_p : M_n)) function findAllOrbitals(p, Φ0, W0, B0, A0, r_max, E_min=0, E_max=(p ? M_p : M_n))

10
test/Pb208_wf.jl
View File

@ -21,14 +21,14 @@ r_max = maximum(xs)
E_min = 880 E_min = 880
E_max = 939 E_max = 939
boundEs = findEs(κ, p, S_interp, V_interp, R_interp, A_interp, r_max, E_min, E_max) approxE = findEs(κ, p, S_interp, V_interp, R_interp, A_interp, r_max, E_min, E_max) |> minimum
groundE = minimum(boundEs) groundE = refineEs(κ, p, S_interp, V_interp, R_interp, A_interp, r_max, [approxE])[1]
println("ground state E = $groundE") println("ground state E = $groundE")
plot_r_max = r_max * 0.75
divs = 50 divs = 50
wf = solveWf(κ, p, groundE, S_interp, V_interp, R_interp, A_interp, plot_r_max, divs) wf = solveWf(κ, p, groundE, S_interp, V_interp, R_interp, A_interp, r_max, divs)
rs = collect(0: plot_r_max/divs : plot_r_max) rs = range(0, r_max, length=divs+1)
gs = wf[1, :] gs = wf[1, :]
fs = wf[2, :] fs = wf[2, :]