Fourier's Transform of the Quantum

Scientific Paper
Title	Fourier\'s Transform of the Quantum
Author(s)	Constantin Antonopoulos
Keywords	Fourier Transform, Quantum Mechanics
Published	2009
Journal	Galilean Electrodynamics
Volume	20
Number	4
Pages	74-80

Abstract

I show that the quantum relations, E = hv and p = h / L are sufficient for deriving the two corresponding uncertainties, and need no help from the Fourier analysis, as is the typical method.  If v involves a period t > 0 that is the minimum time interval needed to define E, then defining E any sooner will introduce an uncertainty in its value proportional to how much sooner.  And if L stands for a minimum distance needed to define p, then defining p in any shorter distance will introduce an uncertainty in its value, proportional to the amount shorter.  Since, however, E is to be defined over t, and not sooner, Et = h. And since p is to be defined over L, and not shorter, pL = h. Hence, altogether,  dEdt, dpdq >= h.  In the Fourier treatment, however, E = hv does not suffice to deduce dEdt >= h; another premise, dvdt >= 1, is equally necessary to the deduction. Inclusion of this extraneous premise literally transforms this uncertainty from a lim-ited, and therefore manageable, energy-time opposition, into an unlimited, and therefore unmanageable, opposition, demanding all kinds of absurdities for its satisfaction, as several reliable commentators have noted since the early 60?s. These problems are inherent in the Fourier approach, but my derivation escapes them.