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Unformatted text preview: PHYS851 Quantum Mechanics I, Fall 2008 HOMEWORK ASSIGNMENT 14 1. [15 pts] Consider the twostate quantum system described by H = H + V , where H = planckover2pi1 2 (  1 )( 1   )(  ) , and V = planckover2pi1 2 (  )( 1  +  1 )(  ) . In the Schrodinger picture we have  S ( t ) ) = c ( t )  ) + c 1 ( t )  1 ) . Solve Schrodingers equation for the coefficients c ( t ) and c 1 ( t ) with the initial conditions c (0) = 1 and c 1 (0) = 0. Let the operator W be defined in the Schrodinger picture as W =  1 )( 1   )(  . Compute ( W ) as a function of time. 2. [20 pts] For the same system as problem 1, compute ( W ) using the Heisenberg picture. Do this by first computing the commutator [ H,W ] and inserting the result into the Heisenberg equation of motion for W . Repeat this procedure to find the equations of motion for whatever operators appear on the RHS of the equation for dW/dt . Try to obtain a closed set of equations (there should be three in all). Solve the this set of equations for the appropriate initial conditions and compare yourthree in all)....
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This note was uploaded on 10/25/2010 for the course PHYSICS PHYS 851 taught by Professor Michaelmoore during the Fall '08 term at Michigan State University.
 Fall '08
 MichaelMoore
 mechanics, Work

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