Question

A. Commutator algebra 1/ Let A and B be two arbitrary observables. Is their commutator Hermitian, unitary, anything else? Justify your answer with a rigorous derivation. 2/ Prove the following relations, where A and B are two arbitrary operators and a, b ? C: [aA, bB] = ab[A, B] [A + B, C] = [A, C] + [B, C] [A, B + C] = [A, B] + [A, C] [A, BC] = B[A, C] + [A, B]C [AB, C] = A[B, C] + [A, C]B

          A. Commutator algebra
1/ Let A and B be two arbitrary observables. Is their commutator Hermitian, unitary, anything else? Justify your answer with a rigorous derivation.
2/ Prove the following relations, where A and B are two arbitrary operators and a, b ? C:
[aA, bB] = ab[A, B]
[A + B, C] = [A, C] + [B, C]
[A, B + C] = [A, B] + [A, C]
[A, BC] = B[A, C] + [A, B]C
[AB, C] = A[B, C] + [A, C]B

A. Commutator algebra
1/ Let A and B be two arbitrary observables. Is their commutator Hermitian, unitary, anything else? Justify your answer with a rigorous derivation.
2/ Prove the following relations, where A and B are two arbitrary operators and a, b ? C:
[aA, bB] = ab[A, B]
[A + B, C] = [A, C] + [B, C]
[A, B + C] = [A, B] + [A, C]
[A, BC] = B[A, C] + [A, B]C
[AB, C] = A[B, C] + [A, C]B

Added by Allen W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ripujeet P

03/21/2022

Step 1

Step 1:** Given the commutator of two arbitrary observables A and B is defined as: \([A,B] = \alpha AB - \beta BA\) ** Show more…

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Let A and B be two arbitrary observables. Is their commutator Hermitian? Unitary? Anything else? Justify your answer with a rigorous derivation. Prove the following relations where A and B are two arbitrary operators and a, b ∈ C: [aA, bB] = ab[A, B] [A + B, C] = [A, C] + [B, C] [A, B + C] = [A, B] + [A, C] [A, BC] = B[A, C] + [A, B]C [AB, C] = A[B, C] + [A, C]B