Compatibility of qunatum measurements

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Homework Help Overview

The discussion revolves around the compatibility of quantum measurements, specifically focusing on the implications of two non-commuting operators A and B. The original poster questions whether the commutator [A,B] applied to any state psi can yield a result of zero.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the nature of the commutator and its implications for different quantum states. The original poster considers the trivial case where psi equals zero and questions if there are other states that could lead to a zero result.

Discussion Status

Some participants have offered hints and suggestions, such as considering specific examples like the commutator [x^2, p] and the role of position eigenstates, indicating a productive exploration of the topic. However, there is no explicit consensus on the existence of states that yield a zero result when applying the commutator.

Contextual Notes

The discussion is constrained by the original poster's uncertainty about the existence of non-trivial states that could satisfy the condition, as well as the general complexity of quantum mechanics principles being examined.

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

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