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A spin half particle is in the state $${S_z} = \frac{{{\hbar ^2}}}{2}.$$  The expectation values of $${S_x},\,S_x^2,\,{S_y},\,S_y^2$$   are given by

A spin half particle is in the state $${S_z} = \frac{{{\hbar ^2}}}{2}.$$  The expectation values of $${S_x},\,S_x^2,\,{S_y},\,S_y^2$$   are given by Correct Answer $$0,\,\frac{{{\hbar ^2}}}{4},\,0,\,\frac{{{\hbar ^2}}}{4}$$

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