Azimuthal Wavefunctions: Showing a constant must be an integer

[lms_89]

Homework Statement

In spherical polars, the azimuthal part of the wavefunction of a particle is

psi(phi) = 1/sqrt[2.pi] . exp[i.m.phi]

where phi is the azimuthal angle. Show m must be an integer.

Homework Equations

I know you are supposed to have a good go at solving the problem first, but this doesn't seem the sort of question you have an equation for. I've tried googling, and asking my friends, and thinking about it, but am panicking a bit because my exam is tomorrow and I still don't know what to do!

The Attempt at a Solution

See above! Any suggestions of even how to start would be really helpful :)

 

[Cyosis]

It follows from the boundary conditions on a sphere $\psi(0)=\psi(2\pi)$. Try to find all values for m for which those boundary values hold.

 

[lms_89]

Ah ok, thanks. I'll have another think about it :)