Consider an arbitrary state 
describing the time evolution
of a particle of mass m in a simple harmonic oscillator with spring
constant 
.
Show by explicit computation that
and
Use Ehrenfest's theorem to show that the average position at time t may always be written
where A and 
are an arbitrary amplitude and phase,
respectively.
Hint: First, determine 
and then give the
most general form of the solution for the resulting differential
equation.
How does this compare with the classical result?