A Modern Approach to Quantum Mechanics · Problem 3.17

Time Evolution — John S. Townsend

Physics — Quantum Mechanics · spin-1-expectation-values

Problem

A spin-1 particle is in the state

|\psi\rangle \xrightarrow{S_z\text{ basis}} \frac{1}{\sqrt{14}}\begin{pmatrix}1\\2\\3i\end{pmatrix}

((a)) What are the probabilities that a measurement of

S_z

will yield the values

\hbar

, 0, or

-\hbar

for this state? What is

\langle S_z\rangle

? ((b)) What is

\langle S_x\rangle

for this state? Suggestion: Use matrix mechanics to evaluate the expectation value. ((c)) What is the probability that a measurement of

S_x

will yield the value

\hbar

for this state?