A Guide to Physics Problems. Part 2. Thermodynamics, Statistical Physics, and Quantum Mechanics

c) To find the average value of the position operator, we first need to show

that

Then

The expectation value of the position operator oscillates in time.

5.20 Switched-on Field (MIT)

a) Operate on the eigenfunction by the kinetic energy term in the Hamil-

tonian:

Consider the factor the 1 must give the eigenvalue and must

cancel the potential energy. These two constraints give the identities

The normalization constant is determined by

b) The solution is given above:

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