A Modern Approach to Quantum Mechanics · Problem 1.14

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

Physics — Quantum Mechanics · determine-spin-state-from-probabilities

Problem

It is known that there is a 36\% probability of obtaining

S_z = \hbar/2

and therefore a 64\% chance of obtaining

S_z = -\hbar/2

if a measurement of

S_z

is carried out on a spin-

\frac{1}{2}

particle. In addition, it is known that the probability of finding the particle with

S_x = \hbar/2

, that is in the state

|{+}\mathbf{x}\rangle

, is 50\%. Determine the state of the particle as completely as possible from this information.