A Modern Approach to Quantum Mechanics · Problem 3.24

Time Evolution — John S. Townsend

Physics — Quantum Mechanics · spin-three-halves-expectation-values

Problem

A spin-

\frac{3}{2}

particle is in the state

|\psi\rangle \xrightarrow{S_z\text{ basis}} N\begin{pmatrix}i\\2\\3\\4i\end{pmatrix}

((a)) Determine a value for

N

so that

|\psi\rangle

is appropriately normalized. ((b)) What is

\langle S_x\rangle

for this state? Suggestion: The matrix representation of

\hat{S}_x

is given in Example 3.4. ((c)) What is the probability that a measurement of

S_x

will yield the value

\hbar/2

for this state? Suggestion: See Problem 3.23.