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Hermite polynomial and transformation 
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#1
Feb1509, 10:23 PM

P: 369

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
Feb1609, 08:17 AM

Sci Advisor
P: 1,256

If you FT a product of two functions of x, you should get a convolution in k space, not a simple product.



#3
Feb1609, 08:30 AM

P: 369




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