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Quantum Physics Problem

  • Thread starter kehler
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1. Homework Statement
Wavefunction = (2/L)^(1/2) * sin(2*pi*x/L) exp(−i2*pi^2*h_bar*t/mL^2)

I calculated the expectation value of momentum to be 0, and expectation value of kinetic energy to be 2*pi^2*h_bar/mL^2 (also found to be it's definite K.E)
Using the momentum operator, the wavefunction was found to have only two possible momentums with equal probability of 0.5: (2*pi*h_bar) and -(2*pi*h_bar)
The wavefunction has probability density peaks at +L/4 and -L/4
The question is:
We set up (in the lab) an ensemble of many such particles, all with the same wavefunction. Describe what you expect to be the results of measurements of their position, momentum and kinetic energy.


3. The Attempt at a Solution
It's a five mark question. I know that the average value of the measurements of their momentum will be 0, and the measurements of their kinetic energy will always yield 2*pi^2*h_bar/mL^2. Also, the particles will also most likely be at either +L/4 and -L/4.
Is there anything else I can conclude using the information above?

Any help with the question above would be much appreciated :). I'm not entirely sure that I got all the calculations correct either. Just started doing QM..
 

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