Introduction to Quantum Mechanics · Problem 4.58

Quantum Mechanics in Three Dimensions — David J. Griffiths

Physics — Quantum Mechanics · spin_measurements

Problem

An electron is in the spin state

\chi = A \begin{pmatrix} 1 - 2i \\ 2 \end{pmatrix}

. (a) Determine the constant

A

by normalizing

\chi

. (b) If you measured

S_z

on this electron, what values could you get, and what is the probability of each? What is the expectation value of

S_z

? (c) If you measured

S_x

on this electron, what values could you get, and what is the probability of each? What is the expectation value of

S_x

? (d) If you measured

S_y

on this electron, what values could you get, and what is the probability of each? What is the expectation value of

S_y