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The Pauli spin matrices in quantum mechanics are A = 1 (: ). - ( ), c- 6 -)- B = C = (You will probably find these called o, oy, 0z in your quantum mechanics texts.) Show that A? = B² = C² = a unit matrix. Also show that any two of these matrices anticommute, that is, AB = -BA, etc. Show that the commutator of A and B, that is, AB – BA, is 2iC, and similarly for other pairs in cyclic order. -

The Pauli spin matrices in quantum mechanics are A = 1 (: ). - ( ), c- 6 -)- B = C = (You will probably find these called o, oy, 0z in your quantum mechanics texts.) Show that A? = B² = C² = a unit matrix. Also show that any two of these matrices anticommute, that is, AB = -BA, etc. Show that the commutator of A and B, that is, AB – BA, is 2iC, and similarly for other pairs in cyclic order. -

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The Pauli spin matrices in quantum mechanics are 0. A = 1 0, B = (* 5). C = (You will probably find these called o, oy, 0z in your quantum mechanics texts.) Show that A? = B² = C² = a unit matrix. Also show that any two of these matrices anticommute, that is, AB = -BA, etc. Show that the commutator of A and B, that is, AB – BA, is 2iC, and similarly for other pairs in cyclic order. -
Transcribed Image Text:The Pauli spin matrices in quantum mechanics are 0. A = 1 0, B = (* 5). C = (You will probably find these called o, oy, 0z in your quantum mechanics texts.) Show that A? = B² = C² = a unit matrix. Also show that any two of these matrices anticommute, that is, AB = -BA, etc. Show that the commutator of A and B, that is, AB – BA, is 2iC, and similarly for other pairs in cyclic order. -
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