Harmonic Oscillator

(See attached file for full problem description)

---
1. Consider a particle moving in a harmonic oscillator potential V(x) = ½ kx2. A solution of the time-dependent Schrodinger equation is

cn n(x)*e –i * E(n) * t / h-bar



where the   n   are harmonic oscillator energy eigenstates.

a. Calculate the energy expectation value and the kinetic energy expectation value
K(t) = <  |  | >

At any given time t, in terms of the constants cn. Show that your answers are real, even if the cn are complex.

b. Let   be the time average of K(t). Show that  = ½ .