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Unformatted text preview: PHYS 507 Homework II (Fall ’06) Assigned: November 17, 2006, Friday. Due: November 26, 2006, Sunday. 1. Consider a state of a particle in 1D having the following positionspace wavefunction ψ ( x ) = N exp  x  a ¶ , where a is a distance and N is an appropriate normalization factor. (a) Find N and then compute the momentumspace wavefunction ˜ ψ ( p ). (b) Compute the probability density for momentum distribution ˜ P ( p ) and sketch a plot of it. Are opposite momenta values ( p and p ) equally probable? (c) Compute Δ x and Δ p and show that the uncertainty relation is satisfied. Hints: (1) You can compute expectation values by using either ψ or ˜ ψ . Use whichever is convenient. (2) Note that h p 2 i = h ψ  p 2  ψ i = h pψ  pψ i =  pψ  2 . As a result, h p 2 i can be computed by using positionspace wavefunction by taking only a single derivative. This is an extremely useful trick....
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This note was uploaded on 02/11/2012 for the course MATH 435 taught by Professor Starg during the Spring '11 term at Al Ahliyya Amman University.
 Spring '11
 starg

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