Harmonic Oscillator Operators?

[scarecrow]

I worked these problems out:

[x, H] = xH - Hx = 0

[p, H] = pH - Hp = non-zero

H is the harmonic oscillator Hamilitonian, x and p are the position and momentum operators, respectively.

My question is, why doesn't p commute with H, but x does?

 

[Epicurus]

If you worked out these explicitly this should be pretty clear. The potential term commutes with x but not with p.

 

[Meir Achuz]

I don't think [H,x]=0.

 

[reilly]

The commutator of X with the KE, p*p/2m, is not zero; the commutator is proportional to p, the momentum.
Regards,
Reilly Atkinson

Harmonic oscillator commutators are discussed in almost any QM text,