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Homework Help: 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
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