A Modern Approach to Quantum Mechanics · Problem 1.12

Rotation of Basis States and Matrix Mechanics — John S. Townsend

Physics — Quantum Mechanics · spin-state-direction

Problem

The state

|\psi\rangle = \frac{1}{2}|{+}\mathbf{z}\rangle + \frac{\sqrt{3}}{2}|{-}\mathbf{z}\rangle

is similar to the one given in Problem 1.10. It is just ``missing'' the

i

. By comparing the state with the state

|{+}\mathbf{n}\rangle

given in Problem 1.3, determine along which direction

\mathbf{n}

the state is spin up. Calculate

\langle S_x\rangle

\langle S_y\rangle

, and

\langle S_z\rangle

for the state

|\psi\rangle

. Compare your results with those of Problem 1.10.