chem120a_ps5_sp07 - Chem 120A Problem Set 5 Out: Sat. March...

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Chem 120A Problem Set 5 Out: Sat. March 17, 2007; Due: Fri. March 23, 2007 1. Consider a particle trapped in a symmetric double well potential under conditions that only the lowest two levels are accessible. In a left/right eigenbasis, the Hamiltonian in the two-level approximation is given by ± ε - - ε ² (1) a) Sketch the potential and relevant energy levels. Describe the effect of each term in the Hamiltonian matrix. b) Find the eigenvalues and eigenvectors of the Hamiltonian in the two-level approximation. Sketch the eigenvectors. c) If the particle is initially localized in the left well, Ψ ( t = 0 ) = ³ ³ L ´ , find the probability P L ( t ) that the particle is localized in the left well at time t > 0. Find the complementary probability P R ( t ) that the particle is localized in the right well at time t > 0 and plot both of these probabilities as a function of t . d) Suppose that the double well is made asymmetric, such that ε now takes values ε 1 and ε 2 in the left and right wells, respectively, with
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This homework help was uploaded on 04/06/2008 for the course CHEM 120A taught by Professor Whaley during the Spring '07 term at University of California, Berkeley.

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chem120a_ps5_sp07 - Chem 120A Problem Set 5 Out: Sat. March...

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