oldexam1 - NAME: MIDTERM EXAM 1 PHYS851 Quantum Mechanics...

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Unformatted text preview: NAME: MIDTERM EXAM 1 PHYS851 Quantum Mechanics I, Fall 2007 1. [30 pts] BRAs, KETs, AND POSTULATES: The Hamiltonian of a physical system is H , and the eigenstates of H are | n ) , such that H | n ) = planckover2pi1 n | n ) . (a) [10 pts] Write an expression for the state of the system at time t , | ( t ) ) , in terms of the initial state | (0) ) and the eigenstates and eigenvalues of H . (b) [5 pts] Using your result from (a) write an expression for the wavefunction ( x,t ) in terms of the unspecified initial state | (0) ) . (c) [5 pts] What is the probability to find the system in the state | n ) at time t ? Write your answer in terms of the unspecified initial state | (0) ) (d) [10 pts] What is the average result of a measurement of the energy of the system at time t , given that the measurement is made on a large number of identical systems, each in the same initial state, | (0) ) ?...
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