(a) Using the matrix representations of Ŝ,, Šy, Š2, show that S., Ŝ, = -iħŜ„. (b) For two general operators, prove that [A, B²] = [A, B] B + B [A, B]. Can the right side always be simplified further? (c) Use the result in the previous problem and Eqn. (2.96) to show that Sz com- mutes with S². (Where S² = S? + S + S?)
(a) Using the matrix representations of Ŝ,, Šy, Š2, show that S., Ŝ, = -iħŜ„. (b) For two general operators, prove that [A, B²] = [A, B] B + B [A, B]. Can the right side always be simplified further? (c) Use the result in the previous problem and Eqn. (2.96) to show that Sz com- mutes with S². (Where S² = S? + S + S?)
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![(a) Using the matrix representations of Ŝ„, Šy, Š2, show that S., Š, = -iħŜ„.
%3D
(b) For two general operators, prove that [A, B²] = [A, B] B + B [A, B]. Can the
right side always be simplified further?
(c) Use the result in the previous problem and Eqn. (2.96) to show that Sz com-
mutes with S². (Where S² = S? + S; + S?)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa957bed-8d63-4ec5-83f0-11dee37c879a%2F13cf4c31-e1c8-4ad1-bd74-949c076bafcf%2Fajieqtf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Using the matrix representations of Ŝ„, Šy, Š2, show that S., Š, = -iħŜ„.
%3D
(b) For two general operators, prove that [A, B²] = [A, B] B + B [A, B]. Can the
right side always be simplified further?
(c) Use the result in the previous problem and Eqn. (2.96) to show that Sz com-
mutes with S². (Where S² = S? + S; + S?)
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