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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 position-space 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 momentum-space 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 position-space 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