A harmonic oscillator has mass and angular frequency

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Wave mechanics in one dimension · Quantum dynamics and its formulations

The Structure of Quantum Mechanics, Ch The oscillator as an algebra

Problem

A harmonic oscillator has mass

m = 4.0\times10^{-27}\,\mathrm{kg}

and angular frequency

\omega = 8.0\times10^{13}\,\mathrm{rad\,s^{-1}}

, with

\hat p_H(t) = i\sqrt{\hbar m\omega/2}\,\big(\hat a_H^\dagger(t) - \hat a_H(t)\big)

and

\hat a_H(t) = \hat a\,e^{-i\omega t}

. ((a)) Write

\langle n-1|\hat p_H(t)|n\rangle

as an explicit function of

t

, keeping only the surviving ladder term. ((b)) Evaluate its magnitude for

n=5