# QM: expectation value of a harmonic oscillator

1. Feb 16, 2009

### ktravelet

first post! but for bad reasons lol

Im trying to find <x> and <p> for the nth stationary state of the harmonic potential: V(x)=(1/2)mw^2x^2

i solved for x: x=sqrt(h/2mw)((a+)+(a-))
so <x> integral of si x ((a+)+(a-)) x si.
therefor the integral of si(n+1) x si + si(n-1) x si.
si(n+1) x si as far as I know is always 0 so this would mean <x>=0?
this same convention would be used for <p>.

sorry for the sloppy work but I'm pretty sure <x>, and <p> shouldnt = 0

2. Feb 16, 2009

### nrqed

welcome!

Your result is correct! They are both zero. You can see it directly if you think in terms of raising and lowering operator since, for any eigenstate |n>, we have

$$\langle n| a | n\rangle = \langle n | a^\dagger | n \rangle = 0$$

3. Feb 16, 2009

### ktravelet

Alright thanks a lot! I have absolutely no idea how to find <T>. If you can give me a pointer in the right direction that would be greatly appreciated. Thank you very much for all the help.