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Unformatted text preview: University of Colorado, Department of Physics PHYS3220, Fall 09, HW#10 due Wed, Oct 28, 2PM at start of class 1. Symmetric potentials (Griffiths, Problem 2.1(c), Total: 10 pts) Prove the following statement: If V ( x ) is an even function (that is, V (- x ) = V ( x )), then the stationary state wave functions ( x ) can always be taken to be either even or odd. 2. Stationary states in an infinite square well (Total: 20 pts) Consider a particle of mass m moving freely between x = 0 and x = a inside an infinite square well potential. The normalized stationary states (eigenstates) were found to be n ( x ) = r 2 a sin nx a with eigenenergies E n = n 2 2 ~ 2 2 ma 2 a) Calculate the expectation values < x > , < p > , < x 2 > and < p 2 > for the n-th stationary state. Explain the physical meaning of your results for < x > and < p > . b Calculate the standard deviations x = < x 2 >- < x > 2 and p = p < p 2 >- < p > 2 for the n-th stationary state. One grows more rapidly than the other as-th stationary state....
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This note was uploaded on 02/27/2012 for the course PHYSICS 3220 taught by Professor Stevepollock during the Fall '08 term at Colorado.
- Fall '08