Massive fermions interacting via a harmonic oscillator in the presence of a minimal length uncertainty relation

B. J. Falaye; Shi Hai Dong; K. J. Oyewumi; K. F. Ilaiwi; S. M. Ikhdair

doi:10.1142/S0218301315500871

Massive fermions interacting via a harmonic oscillator in the presence of a minimal length uncertainty relation

B. J. Falaye, Shi Hai Dong, K. J. Oyewumi, K. F. Ilaiwi, S. M. Ikhdair

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9 Scopus citations

Abstract

We derive the relativistic energy spectrum for the modified Dirac equation by adding a harmonic oscillator potential where the coordinates and momenta are assumed to obey the commutation relation [◯,p] = i(1 + ηp2). In the nonrelativistic (NR) limit, our results are in agreement with the ones obtained previously. Furthermore, the extension to the construction of creation and annihilation operators for the harmonic oscillators with minimal length uncertainty relation is presented. Finally, we show that the commutation relation of the SU(1, 1) ∼ SO(2, 1) algebra is satisfied by the operators ± and ẑ.

Original language	English
Article number	1550087
Journal	International Journal of Modern Physics E
Volume	24
Issue number	11
DOIs	https://doi.org/10.1142/S0218301315500871
State	Published - 1 Nov 2015

Keywords

Dirac equation
formula method
generalized uncertainty relation

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title = "Massive fermions interacting via a harmonic oscillator in the presence of a minimal length uncertainty relation",

abstract = "We derive the relativistic energy spectrum for the modified Dirac equation by adding a harmonic oscillator potential where the coordinates and momenta are assumed to obey the commutation relation [◯,p] = i(1 + ηp2). In the nonrelativistic (NR) limit, our results are in agreement with the ones obtained previously. Furthermore, the extension to the construction of creation and annihilation operators for the harmonic oscillators with minimal length uncertainty relation is presented. Finally, we show that the commutation relation of the SU(1, 1) ∼ SO(2, 1) algebra is satisfied by the operators ± and ẑ.",

keywords = "Dirac equation, formula method, generalized uncertainty relation",

author = "Falaye, {B. J.} and Dong, {Shi Hai} and Oyewumi, {K. J.} and Ilaiwi, {K. F.} and Ikhdair, {S. M.}",

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T1 - Massive fermions interacting via a harmonic oscillator in the presence of a minimal length uncertainty relation

AU - Falaye, B. J.

AU - Dong, Shi Hai

AU - Oyewumi, K. J.

AU - Ilaiwi, K. F.

AU - Ikhdair, S. M.

PY - 2015/11/1

Y1 - 2015/11/1

N2 - We derive the relativistic energy spectrum for the modified Dirac equation by adding a harmonic oscillator potential where the coordinates and momenta are assumed to obey the commutation relation [◯,p] = i(1 + ηp2). In the nonrelativistic (NR) limit, our results are in agreement with the ones obtained previously. Furthermore, the extension to the construction of creation and annihilation operators for the harmonic oscillators with minimal length uncertainty relation is presented. Finally, we show that the commutation relation of the SU(1, 1) ∼ SO(2, 1) algebra is satisfied by the operators ± and ẑ.

AB - We derive the relativistic energy spectrum for the modified Dirac equation by adding a harmonic oscillator potential where the coordinates and momenta are assumed to obey the commutation relation [◯,p] = i(1 + ηp2). In the nonrelativistic (NR) limit, our results are in agreement with the ones obtained previously. Furthermore, the extension to the construction of creation and annihilation operators for the harmonic oscillators with minimal length uncertainty relation is presented. Finally, we show that the commutation relation of the SU(1, 1) ∼ SO(2, 1) algebra is satisfied by the operators ± and ẑ.

KW - Dirac equation

KW - formula method

KW - generalized uncertainty relation

UR - http://www.scopus.com/inward/record.url?scp=84945536440&partnerID=8YFLogxK

U2 - 10.1142/S0218301315500871

DO - 10.1142/S0218301315500871

M3 - Artículo

SN - 0218-3013

VL - 24

JO - International Journal of Modern Physics E

JF - International Journal of Modern Physics E

IS - 11

M1 - 1550087

ER -

Massive fermions interacting via a harmonic oscillator in the presence of a minimal length uncertainty relation

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