Scaled Fourier Transforms and Heisenberg's Uncertainty Principle

• Published in: Journal of the Chinese Chemical Society (Taipei) Vol. 63; no. 1; pp. 145 - 149
• Main Author: Kouri, Donald J.
• Format: Journal Article
• Language: English
• Published: Weinheim WILEY-VCH Verlag 01.01.2016; WILEY‐VCH Verlag; Wiley Subscription Services, Inc
• Subjects: Digital signal processing; Error correction; Fourier transforms; Harmonic oscillators; Heisenberg's uncertainty principle; Particle mass; Quantum mechanics; Quantum theory; Scaled Fourier transform; Uncertainty analysis
• ISSN: 0009-4536; 2192-6549
• DOI: 10.1002/jccs.201500039

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, while correct for digital signal processing, 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. At the recent QSCP XIX, we claimed a procedure of using a scaled Fourier transform 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.