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## Homework Statement

Check that a given momentum space wave function is normalized. I've done the integral, but the result is not dimensionless. Here is the wave function:

[tex]\overline{\phi} = \frac{1}{\pi} ( \frac{2 a_{0}}{\bar{h}})^{3/2} \frac{1}{(1+(a_{0} p / \bar{h})^2)^2}[/tex]

The units of this function are [tex] p^{-3/2} [/tex]. This implies that the normalization should be done over all of momentum space, but I'm getting tripped up because it has been assumed that

**p**= p

**z**, so I don't know how to integrate over eveything. I tried:

[tex] \int^{-\infty}_{\infty} \left|\overline{\phi}\right|^{2} dp = 1[/tex]

and I got

[tex] \frac{5a_{0}^2}{2\bar{h}^2\pi} [/tex]

but that is not dimensionless, nor is it equal to 1. I get the feeling I need to use some kind of delta function, since the wave function vanishes everywhere except along the p_z axis. I can't seem to wrap my head around this, can anyone help? Thanks.