# [x, H]= ?

1. Feb 14, 2006

### Ratzinger

[x, H]= ??

Given the Hamilton operator for the simple harmonic oscilator H, how do I get to [X, H]= ih(P/ m)? I put X in momentum representation, but then I can't get rid of these diff operators. mmh?

2. Feb 14, 2006

### Hurkyl

Staff Emeritus
You don't need to use any representation at all -- just the expression of H in terms of X and P, and the identity XP - PX=k. (I forget what k is. *sigh*)

Last edited: Feb 14, 2006
3. Feb 14, 2006

### George Jones

Staff Emeritus
You don't need to use differential operators - you can work it out using commutators.

Hint:

[A , BC] = B[A , C] + [A , B]C.

Uses this on the [x , p^2] part.

Regards,
George