Discussion7 - Physics 486 Fall 2007 Discussion Problems 7...

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Physics 486 Fall 2007 Discussion Problems 7 1) A particle of mass, m, in the potential, V(x) = ½ m ω 2 x 2 , starts out (at t = 0) in the state 2 2 2 ( ,0) 1 2 m x m x A x e - Ψ = - , for some constant, A . (a) What is the expectation value of the energy, <E>? (b) At some later time, T, the wave function is given by: 2 2 2 ( , ) 1 2 m x m x T B x e - Ψ = + , for some constant, B . What is the smallest possible value of T?
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Physics 486 Fall 2007 2) Based on Griffiths 3.37. The Hamiltonian for a certain three level system in represented by the matrix
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Discussion7 - Physics 486 Fall 2007 Discussion Problems 7...

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