.Solving [X,H] for the SHO Hamiltonian

[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?

thanks in advance

 

[Hurkyl]

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*)

 

[George Jones]

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