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)=$$\int$$A(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:
$$\Delta$$x$$\Delta$$p>h/4$$\Pi$$
but $$\Delta$$x<a/4
=> $$\Delta$$p>h/(4$$\Pi$$$$\Delta$$a)
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).