Wave Functions of a Harmonic Oscillator

Abstract

By means of some special unitary operators, theorems are obtained extending classical properties of of Kennard's packets (classical motion of the center, and periodic time-depencence of $\Delta x$) over all solutions of the oscillator wave equation. These results are also generalized for the quantum field theory. Using a special "functional representation," nonspreading wave packets with classical properties are given for a general free field.