WaveFunctionsAndProbabilityPretest

- b Explain your answer ©2010 Steve Pollock Steve Goldhaber and the Physics Education Group University of Colorado at Boulder The next two

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Wave Functions and Probability Pretest Name: _______________________________________ CU ID: ____________________ For questions 1 and 2 below, you are given a particular (physically reasonable) quantum mechanical wave function, Ψ ( x , t ) of the very specific form Ψ ( x , t ) = f ( x ) e ict where f ( x ) is a real function of x and c is a real constant. Q1: a) Is the “expectation value of x”, <x>, real? A. Definitely yes, at all times t B. Definitely yes at t=0, but at other times it depends (not enough information) C. It depends for any time, even t=0 D. No, at no time will it ever be real b) Explain your answer: Q2: a) What, if anything, can we say about the sign of <x> at time t=0? A. It must be positive B. It could be positive or 0, but it cannot be negative. C. It just depends (not enough information) D. It could be complex, so the sign is not mathematically well-defined.
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Unformatted text preview: b) Explain your answer: ©2010 Steve Pollock, Steve Goldhaber and the Physics Education Group University of Colorado at Boulder The next two questions refer to the normalized wave function, Ψ ( x , t = 0) , which is shown at the right. Q3: a) What, if anything, can we say about <x>? A. It must be zero. B. It must be positive. C. It depends on the size of the peaks. D. It is not well defined because the wave function is not always positive. b) Explain your answer: Q4: a) What, if anything, can we say about the standard deviation of x, σ x ? A. It is exactly zero. B. It must be less than 1. C. It must be greater than 1. D. It is not well defined. b) Explain your answer: ©2010 Steve Pollock, Steve Goldhaber and the Physics Education Group University of Colorado at Boulder...
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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.

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- b Explain your answer ©2010 Steve Pollock Steve Goldhaber and the Physics Education Group University of Colorado at Boulder The next two

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