hw2246sol - Physics 246, Spring 2007 Homework #2 Due in...

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Physics 246, Spring 2007 Homework #2 Due in class, Wednesday, February 7, 2007 Feel free to discuss the problems with me and/or each other. Each student must write up his/her own solutions separately. Each problem is worth 10 points unless otherwise indicated. 1. Libo±, problem 3.17, p. 87. 2. a) Libo±, problem 3.20, p. 87, part a. b) Now take x 1 = x and x 2 = y , with ˆ H = 1 2 m p 2 x + 1 2 m p 2 y . What is ψ ( x, y ) and what are ψ 1 ( x ) and ψ 2 ( y ) in this case? 3. (15 points) A system at t = 0 is in the state ψ ( x, 0) = 1 ( x ) + 2 ( x ) where φ 1 ( x ) and φ 2 ( x ) are real eigenfunctions of the Hamiltonian with eigenvalues E 1 and E 2 and A, B are real. a) Assuming that φ 1 ( x ) and φ 2 ( x ) are properly normalized, what values can A and B take on? (Hint: R φ * 1 φ 2 dx = 0.) b) Show that the probability distribution is of the form P ( x, t ) = f ( x ) + g ( x ) cos ωt . c) What are
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hw2246sol - Physics 246, Spring 2007 Homework #2 Due in...

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