C. Darwin
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Homework Statement
\Psi(x,0) = \frac{1}{\sqrt{L}}, ~~~~~~ \left|x\right| < L/2
At the same instant, the momentum of the particle is measured, what are the possible values, and with what probability?
Homework Equations
The Attempt at a Solution
Well, I know that \Delta{}x = L so can I then say that since \Delta{}p \geq \frac{\hbar}{2L} p must be greater than the same amount?
As far as finding the probability goes, I think I need to do the Fourier transform a(k) = \int_{-L/2}^{L/2} \frac{1}{\sqrt{L}} e^{-ikx} dx = \frac{2}{k\sqrt{L}}sin(\frac{L}{2}k)
Now if I take the square of a(k), how do I normalize it? What are the limits of the integral? If I normalize Psi(x) before I do the Fourier transform, will it be normalized after?