Compatibility of qunatum measurements

1. Dec 16, 2005

sachi

The question is "two operators A,B do not commute". Is it true that
([A,B]psi) does not equal zero for any state psi?"

I'm not sure if there are any cases in which a state psi could produce this result (except for the obvious one where psi = 0 and there is no particle).

Thanks

2. Dec 16, 2005

Physics Monkey

Here is a hint: think about the commutator $$[x^2 , p]$$. Can you find a state that gives zero when you hit it with the commutator even though commutator isn't identically zero?

3. Dec 17, 2005

sachi

I've tried applying the commutator to an arbitrary psi and i get i*h bar * 2x* psi. The only case where I can think of this equalling zero is when psi = 0, which is the obvious case of having no particle.

4. Dec 17, 2005

Physics Monkey

You can't think of any state that gives zero when you hit it with the position operator? Hint: think about position eigenstates.