Relativistic solutions of generalized-Dunkl harmonic and anharmonic oscillators

Hassanabadi, S.; Křı́ž, Jan; Lütfüoğlu, B. C.; Hassanabadi, H.

doi:10.1088/1402-4896/aca2f7

Cited by 16 publications

(7 citation statements)

References 62 publications

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“…The coupling to electromagnetic fields was discussed in [29,30]. For relativistic aspects see [31,32] and references therein.…”

Section: Introductionmentioning

confidence: 99%

On the path integral formulation of Wigner–Dunkl quantum mechanics

Junker

2024

J. Phys. A: Math. Theor.

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Feynman’s path integral approach is studied in the framework of theWigner-Dunkl deformation of quantum mechanics. We start with reviewing somebasics from Dunkl theory and investigate the time evolution of a Gaussian wavepacket, which exhibits the same dispersion relation as observed in standard quantummechanics. Feynman’s path integral approach is then extended to Wigner-Dunklquantum mechanics. The harmonic oscillator problem is solved explicitly. We thenlook at the Euclidean time evolution and the related Dunkl process. This process,which exhibit jumps, can be represented by two continuous Bessel processes, one withreflection and one with absorption at the origin. The Feynman-Kac path integral forthe harmonic oscillator problem is explicitly calculated.

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“…The coupling to electromagnetic fields was discussed in [29,30]. For relativistic aspects see [31,32] and references therein.…”

Section: Introductionmentioning

confidence: 99%

On the path integral formulation of Wigner–Dunkl quantum mechanics

Junker

2024

J. Phys. A: Math. Theor.

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“…The nonrelativistic solution of a position-dependent mass model is examined with a Lie algebraic method in [34]. Recently, we observe papers that consider different generalization forms of Dunkl derivative in the literature [35][36][37]. Dunkl formalism is also employed in noncommutative phase space in [38].…”

Section: Introductionmentioning

confidence: 99%

Ideal Bose Gas and Blackbody Radiation in the Dunkl Formalism

F.¹,

Hamil²,

Lütfüoğlu³

et al. 2023

Preprint

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Recently, deformed quantum systems gather lots of attention in the literature. Dunkl formalism differs from others by containing the difference-differential and reflection operator. It is one of the most interesting deformations since it let us discuss the solutions according to the even and odd solutions. In this work, we studied the ideal Bose gas and the blackbody radiation via the Dunkl formalism. To this end, we made a liaison between the coordinate and momentum operators with the creation and annihilation operators which allowed us to obtain the expressions of the partition function, the condensation temperature, and the ground state population of the Bose gas. We found that Dunkl-condensation temperature increases with increasing θ value. In the blackbody radiation phenomena, we found how the Dunkl formalism modifies total radiated energy. Then, we examined the thermal quantities of the system. We found that the Dunkl deformation causes an increase in entropy and specific heat functions as well as in the total radiation energy. However, we observed *

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“…The dynamics of electrons in a graphene layer which is under the effect of external magnetic field is derived in [55]. There are many more studies in the literature that takes into account the Dunkl formalism as it allows itself to discuss parity-dependent solutions simultaneously [56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73].…”

Section: Introductionmentioning

confidence: 99%