A Modern Approach to Quantum Mechanics · Problem 1.15

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

Physics — Quantum Mechanics · determine-spin-state-from-probabilities-2

Problem

It is known that there is a 90\% probability 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 there is a 20\% probability of obtaining

S_y = \hbar/2

if a measurement of

S_y

is carried out. Determine the spin state of the particle as completely as possible from this information. What is the probability of obtaining

S_x = \hbar/2

if a measurement of

S_x

is carried out?