# Homework Help: Momentum Space Wave Function

1. Oct 3, 2004

### BLaH!

Hey,
We are given the 1s spatial wave function for the hydrogen atom:

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

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

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

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

What should I do? Insert a complete set? Do another transformation? Any help would be appreciated.