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Normalization factor = (-1)^n * Wikipedia

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Nuwan Yapa 2024-02-22 11:26:24 -05:00
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ho_basis.jl
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@ -2,7 +2,7 @@ using NuclearToolkit
using SpecialFunctions using SpecialFunctions
# Gaussian potentials in HO space # Gaussian potentials in HO space
N_nl(n, l) = sqrt(2*factorial(n) / gamma(l + n + 3/2)^3) N_nl(n, l) = (-1)^n * sqrt(1/sqrt(pi) * (1/2)^(l+1) * 2^(n+2*l+3) * factorial(n) / Iterators.prod((2*n+2*l+1):-2:1))
prefactor(n, l, k) = (-1)^k * binomial(n + l + 1/2, n - k) / factorial(k) prefactor(n, l, k) = (-1)^k * binomial(n + l + 1/2, n - k) / factorial(k)
Talmi(l, R, k1, k2) = (1/2) / (1 + 1/R^2)^(3/2 + l + k1 + k2) * gamma(3/2 + l + k1 + k2) Talmi(l, R, k1, k2) = (1/2) / (1 + 1/R^2)^(3/2 + l + k1 + k2) * gamma(3/2 + l + k1 + k2)
V_Gaussian(R, l, n1, n2) = N_nl(n1, l) * N_nl(n2, l) * sum([prefactor(n1, l, k1) * prefactor(n2, l, k2) * Talmi(l, R, k1, k2) for (k1, k2) in Iterators.product(0:n1, 0:n2)]) V_Gaussian(R, l, n1, n2) = N_nl(n1, l) * N_nl(n2, l) * sum([prefactor(n1, l, k1) * prefactor(n2, l, k2) * Talmi(l, R, k1, k2) for (k1, k2) in Iterators.product(0:n1, 0:n2)])