1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple Harmonic Oscillator - Normalization Constant

  1. Oct 8, 2009 #1
    1. The problem statement, all variables and given/known data
    Determine the normalization constants for the harmonic oscillator wavefunctions with v=0, and v=1 by evaluating their normalization integrals and show that they correspond to N=[tex]\frac{1}{\pi^{.5} * 2^v * v!}[/tex]

    2. Relevant equations

    3. The attempt at a solution

    [tex]\int \psi^{2}d\tau[/tex]=1
    [tex]\int \psi^{2}d\tau[/tex] = [tex]\int N^{2}4y^{2}e^{-y^{2}}dy[/tex]=1

    By a table of integrals, integral from 0->inf of y[tex]^{2n}[/tex]exp(-ay[tex]^{2}[/tex]) => ([tex]\frac{(2n!)\pi^{.5}}{2^{2n+1}n!a^{n+1/2}}[/tex])

    So what I end up with is N1=[tex]\sqrt{\frac{1}{\pi^{.5}}}[/tex]

    The given equation of N I evaluate to be [tex]\sqrt{\frac{1}{2\pi^{.5}}}[/tex]

    I've looked through my integration several times, but am not sure where I could be coming up with an error (and checked the formula given by table with various other tables), any help is appreciated.

    EDIT: Noticed that in cartesian, all space is -inf to inf, not 0 to inf as in spherical polar....
    Last edited: Oct 8, 2009
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted