- #1
KFC
- 488
- 4
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?
[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?