1. Not finding help here? Sign up for a free 30min 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!

Momentum Space Wave Function

  1. Oct 3, 2004 #1
    We are given the 1s spatial wave function for the hydrogen atom:

    [tex]\psi(\vec{r}) = \frac{1}{\sqrt{a_{0}^3r}}e^{-r/a_{0}[/tex]

    We are asked to find the momentum space wave function [tex]\phi(\vec{p})[/tex]. Obviously this is just the Fourier transform of the spatial wave function. In calculating [tex]\phi(\vec{p})[/tex] I used the following theorem:

    [tex]For f(\vec{r}) = f(r), \rightarrow F(\vec{q}) = \frac{4\pi}{q}\int_{0}^{\infty} sin(qr) f(r) r dr[/tex]

    Here [tex]F(\vec{q})[/tex] is simply the Fourier transform of [tex]f(\vec{r})[/tex]Anyway, this will give you the momentum space wave function in terms of the magnitude of momentum [tex]p[/tex]. After we find this, how do we find what the probability distribution is for the x-component of momentum [tex]p_{x}[/tex].

    What should I do? Insert a complete set? Do another transformation? Any help would be appreciated.
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted

Similar Discussions: Momentum Space Wave Function
  1. Transverse Waves Help (Replies: 0)