Work out the spin matrices for arbitrary spin s, generalizing spin 1 2 (Equations 4 145 and 4 147), spin 1 (Problem 4 34), and spin 3 2 (Problem 4 61) where Equations 4 145 Sx S h 0 Sy 11 2 2 S 0 S 0 0b0 0 0 0 0 0 00 1 bs 0 by 1 0 0 0 ibs 0 0 ib, 0 ibs 1 0 0 00 0 0 2 S 0 0 bs 1 0 b 2 0 0 0 0 0 0 bs 2 0 0 0 ib 1 0 ibs 2 0 0 0 0 0 ibs 2 0 0 0 0000 O 0 0000 b s l 0 1 5 9 0000 0 ib s l 0 0 ib s 1

Question: Work out the spin matrices for arbitrary spin s, generalizing spin 1/2 (Equations 4.145 and 4.147), spin 1 (Problem 4.34), and spin 3/2 (Problem 4.61).

Work out the spin matrices for arbitrary spin s, generalizing spin 1/2 (Equations 4.145 and 4.147), spin 1 (Problem 4.34), and spin 3/2 (Problem 4.61).

Sx S = h 0 Sy || 11 |2 |2 -S 0 where

Equations 4.145

0 by-1 0 0 0 -ibs 0 0 ib, 0 ibs-1 0

Sx S = h 0 Sy || 11 |2 |2 -S 0 S- 0 0b0 0 0 0 0 : 0 ...00 1 bs 0 by-1 0 0 0 -ibs 0 0 ib, 0 ibs-1 0 0 00 0 0 - 2 S- 0 0 bs-1 0 b-2 : 0 0 : 0 0 *** 0 0 bs-2 0 : 0 0 -ib-1 0 ibs-2 0 0 0 ... ** *** ... ... 0 0 -ibs-2 0 0 0 0000 O... 0 .. 0000 b-s+l 0 *** 1+5-9 0000 0 ib_s+l 0 0 : -ib-s+1

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