# sol3.pdf - Graduate QM(PHYS 519 Problem Set#3 Due Friday...

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Graduate QM (PHYS 519) Problem Set #3 Due Friday. April 14 1. Impulse in Quantum Mechanics A system experiences a perturbation of the form V = ( t ), where W is a Hermitian operator, so the total Hamiltonian H is given by H = H 0 + V . We have H 0 | k i = E k | k i . Suppose that at t < 0 the system was in the n th state of the discrete spectrum. (a) Determine the probabilities for state k 6 = n for t > 0. This requires using a method other than TD FOPT to determine the time evolution operator U ( t ). (b) For small perturbations V , compare your result to the one obtained using TD FOPT. (c) Suppose W = - Px , where P is a constant parameter with dimensions of momen- tum. Find the resulting U ( t ) and relate the result to the title of the problem. 2. Sudden Approximation A particle moving in one dimension ( x ) is in the ground state of an infinitely deep potential well of width a (0 < x < a ).At t = 0 the right wall of the potential moves in a short period of time τ to the point b > a . Find the

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• Spring '13
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