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

Hermite polynomial and transformation

  1. Feb 15, 2009 #1

    KFC

    User Avatar

    In the chapter of quantum harmonic oscillator, we use the Hermite polynomial a lot. And the fourier transformation of Hermite polynomial (in wavenumber space) gives

    [tex]\mathcal{F} \left\{ \exp (-x^2/2) H_n(x) \right\} = (-i)^n \exp (-k^2/2) H_n(k)[/tex]

    Now I need to find the similar result in terms of momentum p, I know the relation between wavenumber and momentum is

    [tex]p = \hbar k[/tex]

    But I still cannot transform above result to that written in terms of p. Any clue?
     
  2. jcsd
  3. Feb 16, 2009 #2

    clem

    User Avatar
    Science Advisor

    If you FT a product of two functions of x, you should get a convolution in k space, not a simple product.
     
  4. Feb 16, 2009 #3

    KFC

    User Avatar

    But I am talking about a special case: Hermite polynomial, so in this case, the above equation is correct. They are just simple product in k space
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Hermite polynomial and transformation
Loading...