A Modern Approach to Quantum Mechanics · Problem 5.21

Wave Mechanics in One Dimension — John S. Townsend

Physics — Quantum Mechanics · density-matrix-pure-mixed-state-conditions

Problem

The density matrix for an ensemble of spin-

\frac{1}{2}

particles in the

S_z

basis is

\hat{\rho} \xrightarrow{S_z \text{ basis}} \begin{pmatrix} \frac{1}{4} & n \\ n^* & p \end{pmatrix}

(a) What value must

p

have? Why? (b) What value(s) must

n

have for the density matrix to represent a pure state? (c) What pure state is represented when

n

takes its maximum possible real value? Express your answer in terms of the state

|{+\mathbf{n}}\rangle

given in Problem 5.19.