Introduction to Quantum Mechanics · Problem 3.15

Formalism — David J. Griffiths

Physics — Quantum Mechanics · uncertainty_principle

Problem

Prove the famous "(your name) uncertainty principle," relating the uncertainty in position (

A = x

) to the uncertainty in energy (

B = p^2/2m + V

\sigma_x \sigma_H \geq \frac{\hbar}{2m} |\langle p \rangle|.

For stationary states this doesn't tell you much—why not?