Question Bank NAT • 1 Mark Section 4: Quantum Mechanics Angular momentum

QB_PH_112: Angular momentum

Question Statement

For an electron in state $|\psi\rangle = \frac{1}{\sqrt{5}}|\uparrow\rangle + \frac{2}{\sqrt{5}}|\downarrow\rangle$, the expectation $\langle S_z \rangle$ in units of $\hbar$ is:
Correct Answer
-0.3, -0.3
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: $\langle S_z \rangle = \frac{\hbar}{2}(1/5 - 4/5) = -0.3\hbar$.
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