Calculate the following commutator [[AB,iℏ], A]

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Homework Help Overview

The discussion revolves around calculating the commutator [[AB,iℏ], A], a problem situated within the context of quantum mechanics and operator algebra.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the definition of the commutator and suggest finding an intermediate commutator before addressing the overall expression. There is an emphasis on substituting definitions into results obtained.

Discussion Status

Some participants have offered guidance on how to approach the problem by breaking it down into smaller components. There appears to be a productive direction in exploring the inner commutator and its implications.

Contextual Notes

Participants are working within the constraints of a textbook problem, which may limit the information available for discussion. The nature of the problem suggests a focus on operator properties in quantum mechanics.

chris1223123
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I've seen this question in a textbook

Calculate the following commutator [[AB,iℏ], A]

I'm not to sure how you go about it i know [A,B] = AB-BA
 
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Let ##C=[AB,i\hbar]##.
Find ##[C,A]##
Substitute the definition for ##C## in the result you got.
 
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kuruman said:
Let ##C=[AB,i\hbar]##.
Find ##[C,A]##
Substitute the definition for ##C## in the result you got.
Thank you! that makes sense
 
You can also start by calculating the inner commutator ##[AB,i \hbar]##.
 
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