Griffiths Quantum Mechanics Problem Set: Homework 10, Assignments of Quantum Physics

Download Griffiths Quantum Mechanics Problem Set: Homework 10 and more Assignments Quantum Physics in PDF only on Docsity! Physics 487 Homework 10 Due November 4, 2005 1. Griffiths 9.2 (p. 341) [5 points] Solve !c a = ! i " H ab ' e ! i"0 tc b , !c b = ! i " H ba ' e i"0 tc a for the case of a time independent perturbation, assuming that ca(0) = 1 and cb(0) = 0. See Griffiths for lengthy comments about this problem. 2. This is Griffiths, problem 9.17 (p. 364) [10 points] A particle starts in the nth state of a square well. Before t = 0, the floor is at V = 0. At t = 0, the floor begins to move up and down: V = V0(t) (a function of time but not position). After t = T, the floor has returned to V = 0. a. Solve for the exact cm(t) using !c m = ! i " c n H mn ' e i E m !E n( )t /" n " . Show that the wave function changes phase, but that no transitions occur. Find the phase change in terms of V(t). b. Analyze the problem using first order perturbation theory and compare the answer with part a. Problem 3 is on the next page.