Confirm Orthogonality of Wavefunctions for Particle in Ring

[myoplex11]

Homework Statement

confirm that wavefunctions for a particle in a ring with different values of of the quantum number m are mutually orthagonal.

Homework Equations

wavefuntion = e^imx


3. The Attempt at a Solution

i know for the 2 wave functions to be orthogonal their integral over the entire range of variables has to equal 1. e^imx * e^i(m+1)x
i don't know how to prove this though

 

[Dick]

If f(x) and g(x) are orthogonal, what you have to prove is that integral of f(x)*conjugate(g(x)) is zero. Not one. That means you want to show that the integral of e^(imx)*e^(-inx) equals zero when integrated from 0 to 2pi when n is not equal to m. Combine the exponentials and find an antiderivative.