Harmonic Oscillators, Heisenberg's Uncertainty Principle and Simultaneous Measurement Precision for Position and Momentum

Abstract

At the recent QSCP XIX, the author claimed a procedure of using a scaled Fourier transform (the scaling being determined by the detailed interaction and particle mass for a harmonic oscillator) to achieve simultaneous resolution of position and momentum greater than the standard Heisenberg value of 1/2. The procedure is, in fact, invalid for quantum mechanics. The purpose of this paper is simply to give the correct analysis of the uncertainty product, thereby clarifying the error made.

This paper has been withdrawn by the author. The claim that a scaled Fourier transform can be used to obtain analysis of quantum harmonic oscillators is incorrect