Even though the observable $S_{y}$ can only have the values $+\frac{1}{2} \hbar$ and $-\frac{1}{2} \hbar$, the expectation value $\left\langle s_{y}\right\rangle$ can have anyvalue between these two extremes.

Question

Quizplus · Accepted Answer

The expectation value $\left\langle s_{y}\right\rangle$ of an observable in quantum mechanics represents the average outcome of many measurements of the observable on a quantum system prepared in the same state. It can indeed take any value between the possible outcomes $+\frac{1}{2} \hbar$ and $-\frac{1}{2} \hbar$, depending on the state of the system.

Even Though the Observable SyS_{y}Sy​ Can Only Have the Values +12ℏ+\frac{1}{2} \hbar+21​ℏ

Even Though the Observable $S_{y}$ Can Only Have the Values $+\frac{1}{2} \hbar$