Expansion of the wave equation for a stationary wave

[John Greger]

Homework Statement

A generic state represented by the wave function $\psi (\vec(x)$ can be expanded in the eigenstates with defined angular momentum. Write such an expansion for a plane wave traveling along the z direction with momentum $p = \hbar k$ in terms of unknown coefficients $c ( k ′ )_ {l m}$ . Show that ##c ( k )_{ l m} are non-zero only if k' = k and m = 0

Homework Equations

The Attempt at a Solution

I don't know where to start. I could of course go the long way, introducing dimensionless variables, do a power series ansatz and solve de DE with frobinious trick. But it seems the answer will be way easier than that if you just know how to approach it.

 

[Keith_McClary]

Have you searched like this?:
https://www.google.ca/search?q=plane+wave+spherical+coordinates