QM · Ch 2 · QHO ground state: σ_x σ_p = ℏ/2

Physics · Quantum Mechanics · Griffiths Ch 2

Problem

For the 1D quantum harmonic oscillator with frequency

\omega

, compute

\langle x^2 \rangle

and

\langle p^2 \rangle

in the ground state

|0\rangle

, then verify that

\sigma_x\sigma_p = \hbar/2

(saturates the Heisenberg bound).