Particle in a cavity in one-dimensional bandlimited quantum mechanics

K. Sailer, Z. Péli, S. Nagy

Research output: Contribution to journalArticle

Abstract

The effects of the generalized uncertainty principle (GUP) on the low-energy stationary states of a particle moving in a cavity with no sharp boundaries are determined by means of the perturbation expansion in the framework of onedimensional bandlimited quantum mechanics. A realization of GUP resulting in the existence of a finite ultraviolet (UV) wave-vector cutoff K ∼ 1/ℓP (with the Planck length ℓP) is considered. The cavity of the size ℓ 蠑 ℓP is represented by an infinitely deep trapezoid-well potential with boundaries smeared out in a range R satisfying the inequalities ℓ 蠑 R ≳ ℓP. In order to determine the energy shifts of the low-lying stationary states, the usual perturbation expansion is reformulated in a manner that enables one to treat consistently order-by-order the direct and indirect GUP effects, i.e., those due to the modification of the Hamiltonian and the lack of the UV modes, respectively. It is shown that the leading terms of the indirect and the direct GUP effects are of the first and second order, respectively, in the small parameter ℓP/ℓ in agreement with our previous finding in a more naive approach Sailer et al (2013 Phys. Rev. D 87 084056).

Original languageEnglish
Article number075305
JournalJournal of Physics A: Mathematical and Theoretical
Volume48
Issue number7
DOIs
Publication statusPublished - Feb 20 2015

Fingerprint

Generalized Uncertainty Principle
Quantum theory
Quantum Mechanics
quantum mechanics
Cavity
cavities
Perturbation Expansion
Stationary States
Ultraviolet
trapezoids
Trapezium or trapezoid
Hamiltonians
perturbation
expansion
Potential Well
Energy
Small Parameter
Electron energy levels
cut-off
First-order

Keywords

  • Bandlimited quantum mechanics
  • Generalized uncertainty principle
  • Minimal length uncertainty

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Modelling and Simulation
  • Statistics and Probability

Cite this

Particle in a cavity in one-dimensional bandlimited quantum mechanics. / Sailer, K.; Péli, Z.; Nagy, S.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 48, No. 7, 075305, 20.02.2015.

Research output: Contribution to journalArticle

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