Momentum Real Space - Possible Values & Probabilities

[Sasuke]

Homework Statement

Suppose at t = 0, a system is in a state given by the wavefunction,
\Psi(x,0)=1/\sqrt{a} for |x|<a/2
and \Psi(x,0)=0 otherwise
If, at the same instant, the momentum of the particle is measured, what are the
possible values that can be found and with what probability?

Homework Equations

Fourier transformations b/w momentum and real spaces
\Psi(x,0)=\intA(k)e^ikxdk
A(k)=\frac{1}{2\Pi}\int\Psi(x,0)e^-ikxdx

The Attempt at a Solution

I have little idea of how to solve this problem. I know that the wave packet is a superposition of waves but i have no idea how to get momentum values. Here is my pathetic fail attempt:
\Deltax\Deltap>h/4\Pi
but \Deltax<a/4
=> \Deltap>h/(4\Pi\Deltaa)
I know its seriously wrong.

 

[javierR]

The A(k) can be viewed as probability amplitudes in momentum space. That is A*(k)A(k) is the probability for a value k. So calculate these things and when you do ask yourself what the form of the expressions can tell you about the range k can have (and what happens at special values of k).