Introduction to Quantum Mechanics · Problem 4.57

Quantum Mechanics in Three Dimensions — David J. Griffiths

Physics — Quantum Mechanics · uncertainty_principle

Problem

Consider the observables

A = x^2

and

B = L_z

. (a) Construct the uncertainty principle for

\sigma_A \sigma_B

. (b) Evaluate

\sigma_B

in the hydrogen state

\psi_{n\ell m}

. (c) What can you conclude about

\langle xy\rangle

in this state?