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When one writes a wavefunction with coordinates as arguments, one works in the coordinate representation. It is also possible to work in the momentum representation: the momenta are then the arguments. If y(x) is a wavefunction in the coordinate representation and j(p) the same wavefunction in momentum representation then
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1
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dx ei2ppx/hy(x), |
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dp e-i2ppx/hj(p). |
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a) Write the following wavefunctions in momentum representation.
with n = 1,2,3,.... These are solutions of the Schrödinger equation for a particle in a box with walls at x = 0 and x = a
b) Calculate
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dp pm|j1(p)|2 |
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dp pm|j1(p)|2 |
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for m = 1 and m = 2. Compare the results with the expectation values for p and p2.
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