Some consequences of GUP induced ultraviolet wavevector cutoff in one-dimensional Quantum Mechanics

TL;DR

This paper explores how a GUP-induced ultraviolet wavevector cutoff affects one-dimensional quantum mechanics, revealing modifications in wavepacket dynamics and energy levels, with implications for quantum theory at small scales.

Contribution

It introduces a projection method to handle the GUP-induced UV cutoff and analyzes its effects on wavefunctions and energy spectra in one-dimensional quantum systems.

Findings

Bandlimitation alters wavepacket speed and spreading.

GUP with bandlimitation causes less suppressed deviations in energy levels.

A unique coordinate representation is derived from discrete samples.

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.