Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Particle in a ring

  1. Oct 7, 2008 #1
    1. The problem statement, all variables and given/known data
    confirm that wavefunctions for a particle in a ring with different values of of the quantum number m are mutually orthagonal.

    2. Relevant 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 dont know how to prove this though
  2. jcsd
  3. Oct 7, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook