Some consequences of the generalized uncertainty principle induced ultraviolet wave-vector cutoff in one-dimensional quantum mechanics

K. Sailer, Z. Péli, S. Nagy

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3 Citations (Scopus)

Abstract

A projection method is proposed to treat the one-dimensional Schrödinger equation for a single particle when the generalized uncertainty principle (GUP) generates an ultraviolet (UV) wave-vector cutoff. The existence of a unique coordinate representation called the naive one is derived from the one-parameter family of discrete coordinate representations. In this bandlimited quantum mechanics a continuous potential is reconstructed from discrete sampled values observed by means of a particle in maximally localized states. It is shown that bandlimitation modifies the speed of the center and the spreading time of a Gaussian wave packet moving in free space. Indication is found that GUP accompanied by bandlimitation may cause departures of the low-lying energy levels of a particle in a box from those in ordinary quantum mechanics to be much less suppressed than commonly thought when GUP without bandlimitation is at work.

Original languageEnglish
Article number084056
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume87
Issue number8
DOIs
Publication statusPublished - Apr 22 2013

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ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)

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