Harmonic Oscillator Wave Functions

Abstract

A harmonic oscillator wave packet which oscillates sinusoidally without change in shape has been described by Schrödinger and others. It is shown in the present note that there are an infinite number of such wave packets—of which the above is a special one-having the shapes of the various eigenfunctions of the harmonic oscillator Hamiltonian. The relation of these wave packets to the classical oscillator is discussed.