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

The has a frequency and eigenvalues

where is an integer. The oscillator has a frequency of

and eigenvalues where is an integer.

5.18 Time-Dependent Harmonic Oscillator I

(Wisconsin-Madison)

a) At times the wave function is

b) The state has even parity: it remains the same if one replaces

by since This is true for all times.

c) The average value of the energy is

which is independent of time.

5.19 Time-Dependent Harmonic Oscillator II

(Michigan State)

a) The time dependence of the wave function is

b) The expectation value for the energy is

which is independent of time.

QUANTUM MECHANICS 263