Introduction to Quantum Mechanics · Problem 3.16

Formalism — David J. Griffiths

Physics — Quantum Mechanics · compatible_observables

Problem

Show that two noncommuting operators cannot have a complete set of common eigenfunctions. Hint: Show that if

\hat{P}

and

\hat{Q}

have a complete set of common eigenfunctions, then

[\hat{P}, \hat{Q}] f = 0

for any function in Hilbert space.