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Scaled Fourier Transforms and Heisenberg’s Uncertainty Principle
Author(s) -
Kouri Donald J.
Publication year - 2016
Publication title -
journal of the chinese chemical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 45
eISSN - 2192-6549
pISSN - 0009-4536
DOI - 10.1002/jccs.201500039
Subject(s) - uncertainty principle , fourier transform , scaling , resolution (logic) , product (mathematics) , harmonic oscillator , position (finance) , quantum mechanics , chemistry , quantum , physics , mathematics , geometry , artificial intelligence , computer science , finance , economics
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.