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BergEC-jl
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Nuwan Yapa 2024-02-22 20:12:41 -05:00
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ho_basis.jl
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@ -4,7 +4,7 @@ using SpecialFunctions
# Gaussian potentials in HO space
sqrt_factorial(n) = Iterators.prod(sqrt.(n:-1:1))
sqrt_double_factorial(n) = Iterators.prod(sqrt.(n:-2:1))
N_nl(n, l) = (-1)^n * sqrt_factorial(n) * sqrt(1/sqrt(pi) * (1/2)^(l+1) * 2^(n+2*l+3)) / sqrt_double_factorial(2*n+2*l+1)
N_nl(n, l) = (-1)^n * sqrt_factorial(n) * sqrt(1/sqrt(pi) * 2^(n+l+2)) / sqrt_double_factorial(2*n+2*l+1)
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)
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)])