(1-x^2) (d^2P/dx^2) - 2x (dP/dx) + l(l+1) P = 0
l being the total angular momentum quantum number, and P being the solution to the theta part of the eigenfunction from the schrodinger equation after using separation of variables, with x=cos theta
I found the first solution type, say y1...
Hi all,
I've been doing a math problem about the Legendre differential equation, and finding there are two linearly independent solutions. When I was taught about quantum mechanics the polynomial solutions were introduced to me as the basis for spherical harmonics and consequently the...