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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


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    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.
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