Robert Mann - An Introduction to Particle Physics and the Standard Model · Problem 5.8

Accelerators — Robert Mann

Physics — Particle Physics · spin-measurements-electron-state

Problem

Suppose an electron is in the state

\psi = \alpha\begin{pmatrix}1\\0\end{pmatrix} + \beta\begin{pmatrix}0\\1\end{pmatrix}

. (a) What relationship must

\alpha

and

\beta

obey in order for

\psi

to be normalized? (b) What values might be obtained upon measurement of

S_x

, and what is the probability of each? (c) What values might be obtained upon measurement of

S_y

, and what is the probability of each? (d) What values might be obtained upon measurement of

S_z

, and what is the probability of each?