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

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To calculate the commutator [[AB, iℏ], A], start by defining C as [AB, iℏ]. The first step involves finding the inner commutator [AB, iℏ], which simplifies the process. After determining C, substitute it back into the expression to find [C, A]. This method clarifies the calculation and leads to the desired result efficiently. Understanding these steps is crucial for solving similar commutator problems 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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