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Unformatted text preview: PHYS852 Quantum Mechanics II, Spring 2010 HOMEWORK ASSIGNMENT 13 Topics covered: Hilbertspace Frame Transformations, TimeDependent Perturbation Theory 1. The Hamiltonian for a driven twolevel system is H = planckover2pi1  2 )( 2  + planckover2pi1 cos( t ) (  1 )( 2  +  2 )( 1  ) , (1) where is the separation between the bare levels, and is the driving frequency. (a) Make a frame transformation generated by the operator G = planckover2pi1  2 )( 2  , and determine the equation of motion for the statevector in the new frame, defined by  G ( t ) ) = U G ( t )  ( t ) ) . (b) Make the rotating wave approximation (RWA) by assuming that , and dropping any terms that oscillate at or near 2 . Write, in terms of the detuning = , the effective timeindependent Hamiltonian, H G , that then governs the time evolution of  G ( t ) ) . (c) Assume that the system begins at time t = 0 in the groundstate of H G , and calculate  G ( t ) ) . Is this a stationary state in the rotating frame? Now use  S ( t ) ) = U G ( t )  G ( t ) ) to see what this state looks like in the Scrodinger picture. Is it a stationary state in theto see what this state looks like in the Scrodinger picture....
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This note was uploaded on 12/21/2011 for the course PHYS 852 taught by Professor Moore during the Spring '11 term at Michigan State University.
 Spring '11
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