Question

Anyone able to help work through a spherical harmonics question? Setting up in comments..

Answer 1

\[\Delta \Psi(r, \theta, t) = \sum_{}^{} f(t) R(r) \Theta(\theta)\]

Answer 2

My question is phi independent and I'd like to apply the laplacian to determine my eigenfunctions and eigenvalues

Answer 3

I'm fairly certain I end up with the Legendre Polynomials and R(r) = A r^l. But I would like to work through it to prove it