A Modern Approach to Quantum Mechanics · Problem 1.10

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

Physics — Quantum Mechanics · spin-state-expectation-values

Problem

The state

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

is a state with

S_n = \hbar/2

along a particular axis

\mathbf{n}

. Compare the state

|\psi\rangle

with the state

|{+}\mathbf{n}\rangle

in Problem 1.3 to find

\mathbf{n}

. Determine

\langle S_x\rangle

\langle S_y\rangle

, and

\langle S_z\rangle

for this state. Note:

\langle S_z\rangle

and

\langle S_y\rangle

for this state are given in Example 1.2 and Example 1.3, respectively.