348-problem41 - Calculate the survival probability for a...

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Chem. 540 Instructor: Nancy Makri PROBLEM 41 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.
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Unformatted text preview: Calculate the survival probability for a harmonic oscillator which at t = is prepared a) in the ground eigenstate Φ of the Hamiltonian, and b) in a superposition of the ground and first excited eigenstates, i.e., for the initial state ( 29 1 2 1 (0) 2-Ψ = Φ + Φ . Compare your results and comment. ....
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