6. The Pauli spin matrices in quantum mechanics are A = (? :). B= (? 5). c= (G -). c = (6 -). A = (You will probably find these called oz, oy, oz 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.
6. The Pauli spin matrices in quantum mechanics are A = (? :). B= (? 5). c= (G -). c = (6 -). A = (You will probably find these called oz, oy, oz 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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Transcribed Image Text:6.
The Pauli spin matrices in quantum mechanics are
A = (? :). B= (? 5). c= (G -).
c = (6 -).
A =
(You will probably find these called oz, oy, oz 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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