Dirac equation for hyrdogen atom

[ohno]

Implement the module of :DiracHyrdogen. Find an appropriate reference from the candidates or Wikipedia.

The spherical harmonics have already been used in the hydrogen atom.

Antique.jl/src/HydrogenAtom.jl

Lines 32 to 39 in 2994e17

	# Spherical Harmonics
	function Y(θ, φ; l=0, m=0)
	N = (im)^(m+abs(m)) * sqrt( (2*l+1)*factorial(l-Int(abs(m))) / (2*factorial(l+Int(abs(m)))) )
	return N * P(cos(θ),n=l,m=Int(abs(m))) * exp(im*m*φ) / sqrt(2*π)
	end
	# Associated Legendre Polynomials
	P(x; n=0, m=0) = (1//2)^n * (1-x^2)^(m//2) * sum(j -> (-1)^j * factorial(2*n-2*j) // (factorial(j) * factorial(n-j) * factorial(n-2*j-m)) * x^(n-2*j-m), 0:Int(floor((n-m)/2)))