**Probability density for momentum**
I am having a little difficulty with problem 9 on the attached problem set.
Consider a particle moving in 1D, in an initial wave function of the form
psi(x,0)=psi(x)=A exp(-a(x-x0)^2) exp(ik0 x)
a) Determine the value of the normalization constant A so that the state is appropriately normalized
b) Determine the probability density rho(k) that a measurement on this state of the particle's momentum will yield the value p_k = hbar k. What is the probable value that would be obtained in such a measurement?
I hopefully calculated the value of A correctly with a gaussian integral. Please verify that A is correct.
I am stuck on part b. Perhaps I did not calculate dell correctly? How would I determine the most probable value?
Thanks for any hints on how to proceed or comments on where I might have gone wrong. I have not typed this problem formally but the equations are formatted.
My professor verified that I have the correct answer for part a, however my original approach to part b was incorrect.
I am attaching my latest effort but I really need help.
I need to multiply through by exp(-ikx) and take the Fourier transform, then integrate over all space.
However in the class notes, the original equation for psi was always in integral form over k-space.
My professor's comment was that the Fourier transform of |psi|^2 is not the same as |Fourier transform psi|^2
Do I need to differentiate the original equation first, before multiplying by exp(-ikx)?
Thank you.
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Last edited by roger; Feb 8th 2015 at 07:04 AM.
Reason: New approach to solving problem
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