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Spin Angular Momentum

8.6. a. A particle has s=3/2. The operator S++ is defined to be the square of the raising operator: S++ = (S+)^2, where S+ is the usual raising operator:
S+|sms = h (s(s+1) - ms(ms+1)|sms +1)^1/2

Derive the matrix corresponding to the operator S++.

b. What is the matrix corresponding to the adjoint operator (S++)?

See attachment for better symbol representation.

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This in-depth solution has step-by-step calculations to derive the matrix corresponding to the operator and the adjoint operator of S++.