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quiz01sol - ECE 4060 Introduction to Quantum and...

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1 ECE 4060: Introduction to Quantum and Statistical Mechanics Quiz 1 Solution Prob. 1. Given a wave function of a free particle at t = 0 as: () () = otherwise x x ik A x 0 1 1 exp 0 , 0 ψ (a) Find A . (5 pts) By normalization requirement of = 1 * dx ψ ψ , 2 1 = A . (b) Graphically illustrate () ( ) 2 0 , 0 , x x P = and Re ( (x,0)), assuming 0 < k 0 < 1. (10 pts) (c) Assuming a dispersion relation of m k 2 2 h = ω , graphically illustrate P(x, t) and Re ( (x,t)) (10 pts) (*** Due to a critical error in Homework 2, this problem will not count. ***) Prob. 2. Given a wave function of a free particle at t = 0 as: () () () 2 1 2 1 exp 2 1 exp 2 3 0 , k k x ik x ik x + = P(x,0) Re ( (x,0)) x x P(x,t) Re ( (x,t)) x x 1/2 1 1 1 1 2 / 1
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2 (a) What is the expectation value of momentum p ˆ at t = 0 ? (10 pts) 2 1 4 1 4 3 | ˆ | k k p h h + = ψ (b) If we measure the momentum at t = 0 , what are the possible outcome? What are the probabilities of obtaining those outcome? Briefly explain.
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This note was uploaded on 10/25/2009 for the course ECE 4060 at Cornell.

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quiz01sol - ECE 4060 Introduction to Quantum and...

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