- #1
Sasuke
- 4
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Homework Statement
Suppose at t = 0, a system is in a state given by the wavefunction,
[tex]\Psi[/tex](x,0)=1/[tex]\sqrt{a}[/tex] for |x|<a/2
and [tex]\Psi[/tex](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
[tex]\Psi[/tex](x,0)=[tex]\int[/tex]A(k)eikxdk
A(k)=[tex]\frac{1}{2\Pi}[/tex][tex]\int[/tex][tex]\Psi[/tex](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:
[tex]\Delta[/tex]x[tex]\Delta[/tex]p>h/4[tex]\Pi[/tex]
but [tex]\Delta[/tex]x<a/4
=> [tex]\Delta[/tex]p>h/(4[tex]\Pi[/tex][tex]\Delta[/tex]a)
I know its seriously wrong.