The discussion centers on the commutator property defined as [A,BC] = [A,B]C + B[A,C]. It is established that if B equals C, then the expression [A,B]C + B[A,C] simplifies to [A,B](C+B). The commutator is explicitly defined as [A,B] = AB - BA. The participants clarify that since the operators A, B, and C do not commute, the order of operations cannot be switched, leading to the conclusion that the left-hand side does not equal the right-hand side without additional conditions.
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The commutator (in the assumed context above) is defined as ##[A,B]=AB-BA##.Kyle Nemeth said:Given the property,
[A,BC] = [A,B]C+B[A,C],
is it true that, if B=C, then
[A,B]C+B[A,C]=[A,B]C+B[A,B]=[A,B](C+B)?
I apologize if I have posted in the wrong forum.