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

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SUMMARY

The discussion focuses on calculating the commutator [[AB, iℏ], A]. Participants clarify that the first step involves defining C as [AB, iℏ] and then finding the commutator [C, A]. The definition of the commutator [A, B] = AB - BA is emphasized as a crucial part of the calculation. The approach suggests starting with the inner commutator [AB, iℏ] before proceeding to the outer commutator.

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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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