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 Quantum Physics Quantum Physics Help Forum Feb 6th 2015, 02:41 PM   #1
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Location: Greater St. Louis area
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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.
Attached Files homework3.pdf (57.6 KB, 3 views) HW3_9b.pdf (301.2 KB, 2 views)

Last edited by roger; Feb 8th 2015 at 07:04 AM. Reason: New approach to solving problem   Feb 11th 2015, 01:17 PM   #2
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Join Date: Feb 2013
Location: Greater St. Louis area
Posts: 43

Although I did not receive any replies, I am posting my solutions and my professors answers in case anyone is searching in the future.
Attached Files homework3.pdf (57.6 KB, 2 views) HW3.pdf (244.8 KB, 3 views)  Tags density, momentum, probability Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post pixiv Quantum Physics 3 Jan 3rd 2014 04:25 PM tadkins Advanced Thermodynamics 0 Sep 10th 2012 09:21 AM alexgeek Kinematics and Dynamics 2 Jan 20th 2011 02:40 PM mypetbuffalo Thermodynamics and Fluid Mechanics 0 Jan 12th 2010 03:56 PM synclastica_86 Quantum Physics 1 May 14th 2009 10:02 PM