Some consequences of GUP induced ultraviolet wavevector cutoff in one-dimensional Quantum Mechanics
Abstract
A projection method is proposed to treat the one-dimensional Schrodinger equation for a single particle when the Generalized Uncertainty Principle (GUP) generates an ultraviolet (UV) wavevector 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 wavepacket 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 much less suppressed than commonly thought when GUP without bandlimitation is in work.
Keywords
Cite
@article{arxiv.1301.6913,
title = {Some consequences of GUP induced ultraviolet wavevector cutoff in one-dimensional Quantum Mechanics},
author = {K. Sailer and Z. Peli and S. Nagy},
journal= {arXiv preprint arXiv:1301.6913},
year = {2015}
}
Comments
20 pages, 2 figures