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Compatibility of qunatum measurements 
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#1
Dec1605, 05:41 PM

P: 75

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
Dec1605, 06:20 PM

Sci Advisor
HW Helper
P: 1,334

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



#3
Dec1705, 04:39 PM

P: 75

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.



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