542-problem-1 - probability for a harmonic oscillator which...

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Chem. 542 Assignment by Nancy Makri PROBLEM 1 The survival amplitude for a system initially described by the state (0) Ψ is defined as ( ) ( ) (0) C t t = Ψ Ψ i.e., ( ) C t is a measure of the overlap of the propagated state with the initial one. The survival probability ( ) P t is defined as the absolute square of the survival amplitude. Calculate the survival
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Unformatted text preview: probability for a harmonic oscillator which at t = is prepared a) in the ground eigenstate of the Hamiltonian, b) in the first excited state 1 , and c) in a superposition of the ground and first excited eigenstates, i.e., for the initial state ( 29 1 2 1 (0) 2- = + . Compare your results and comment. ....
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This note was uploaded on 02/08/2012 for the course CHEM 542 taught by Professor Gruebele during the Spring '08 term at University of Illinois, Urbana Champaign.

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