- #1

arenaninja

- 26

- 0

## Homework Statement

A particle mass m in the harmonic oscillator potential starts out in the state [tex]\psi(x,0)=A\left(1-2\sqrt(\frac{m\omega}{\hbar})x\right)^{2}e^{\frac{-m\omega}{2\hbar}x^{2}}[/tex] for some constant A.

a) What is the expectation value of the energy?

b) At some time later T the wave function is [tex]\psi(x,T)=B\left(1+2\sqrt(\frac{m\omega}{\hbar})x\right)^{2}e^{\frac{-m\omega}{2\hbar}x^{2}}[/tex]

## Homework Equations

I used ladder operators (wayyy better than doing integrals, though I figured that out only minutes ago).

## The Attempt at a Solution

I solved that the constant A should be [tex]\frac{1}{5}\left(\frac{m\omega}{\pi\hbar}\right)^{1/4}[/tex], but apparently it wasn't needed.

For part a I got [tex]\frac{\hbar\omega}{2}\left(2n+1\right)[/tex], which has units of energy so it could be ok. But part b has me baffled. Neither equation has a time dependence, so I have no clue what T should be. I do notice that the constant has changed, and that there seems to be a sign reversal. Unfortunately I'm stuck as to how this would help me resolve what T should be.