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## Homework Statement

A particle of mass ##m## is trapped between two walls in an infinite square well with potential energy

[tex]V(x) = \left\{ \begin{array}{cc} +\infty & (x < -a), \\ 0 & (-a \leq x \leq a), \\ +\infty & (x > a).\end{array} \right.[/tex]

Suppose the wavefuntion of the particle at time ##t=0## is [tex]\psi(x) = \frac{1}{\sqrt{2a}}.[/tex]

Show that the probability density for the particle having momentum ##p## is [tex]g(p) = \frac{\sin^2 (pa)}{(\pi a p)^2} \qquad (-\infty < p < +\infty).[/tex]

## Homework Equations

## The Attempt at a Solution

I know that to transform the wave function to momentum representation I use [tex] \phi(p) = \frac{1}{\sqrt{2\pi}} \int_{-a}^a \psi(x) e^{-ipx/\hbar}\,dx.[/tex] From this I got [tex]\phi(p) = \frac{\hbar \sin(pa/\hbar)}{p\sqrt{\pi a}}.[/tex] Squaring this isn't going to give the required answer though. Any help appreciated. Thanks.