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## Homework Statement

The Fourier transfrom of the wave function is given by

$$\Phi(p) = \frac{N}{(1+\frac{a_0^2p^2}{\hbar^2})^2}$$

where ##p:=|\vec{p}|## in 3 dimensions.

Find N, choosing N to be a positive real number.

## Homework Equations

$$\int d^3\vec{p}|\Phi(p)|^2=1$$

, over all p in the 3 dimensions.

## The Attempt at a Solution

First finding the complex conjugate,

$$\Phi^*(p) = \frac{N}{(1+\frac{a_0^2 p^2}{\hbar^2})^2}$$

So,

$$|\Phi(p)|^2 = \frac{N^2}{(1+\frac{a_0^2 p^2}{\hbar^2})^4}$$

So,

$$\frac{1}{N^2} = \int d^3 \vec{p}\frac{1}{(1+\frac{a_0^2 p^2}{\hbar^2})^4}$$

How would I change ##d^3\vec{p}## to be a triple integral, one of which is over dp?

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