The solution to the Schrodinger equation for the hydrogen atom is:
Ψnlm=A(nar)le−r/naYlm(θϕ)v(nar)
where the function v(x) can be expressed in terms of the polynomials of Laguerre as:
a) Use the relation of orthogonality:
∫0[infinity]Lαk(x)Lαk(x)xk+1e−xdx=α!(α+k)!(2α+k+1)
of the associated polynomials of Laguerre to find the normalization constant A