Exact energy spectrum of the generalized Dirac oscillator in an electric field

In this paper, the propagator of a two-dimensional Dirac oscillator in the presence of a uniform electric field is derived by using the path integral technique. The fact that the globally named approach is used in this work redirects, beforehand, our search for the propagator of the Dirac equation to that of the propagator of its quadratic form. The internal motions relative to the spin are represented by two fermionic oscillators, which are described by Grassmannian variables, according to Schwinger’s fermionic model. Once the integration over the anticommuting variables (Grassmannian variables) is accomplished, the problem becomes the one of finding a non-relativistic propagator with only bosonic variables. The energy spectrum of the electron and the corresponding eigenspinors are also obtained in this work.

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“…and the energies E ,s py,n of our system are In the particular case, when p y = 0, this result agrees exactly with that of Ref. 43.…”

Section: Exact Calculation For the Green's Functionsupporting

confidence: 92%

“…In this regard, it is worth mentioning that the general Dirac oscillator subjected to a non-uniform electric field was studied in Ref. 43. It was found, in this reference, that in the case of specially chosen electric field, the eigenvalue equation can be resolved exactly.…”

Section: Introductionmentioning

confidence: 98%

Dirac oscillator in a uniform electric field: Path integral treatment

Bada

Aouachria

2019

Mod. Phys. Lett. A

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“…Such oscillators, initially introduced as systems linear in momentum and coordinate variables [29], are closely related to Dirac models coupled to magnetic fields. Applications include experimental realizations of Dirac oscillators [17], their coupling to electric fields [23], and within a rotating reference frame [39]. Interestingly, it has been shown that in (2 + 1) dimensions the Dirac oscillator is equivalent to a spin 1/2 particle in a magnetic field [11].…”

Section: Introductionmentioning

confidence: 99%

Dirac systems with magnetic field and position dependent mass: Darboux transformations and equivalence with generalized Dirac oscillators

Schulze-Halberg,

Roy

2021

Preprint

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We construct a Darboux transformation for a class of two-dimensional Dirac systems at zero energy. Our starting equation features a position-dependent mass, a matrix potential, and an additional degree of freedom that can be interpreted either as a magnetic field perpendicular to the plane or a generalized Dirac oscillator interaction. We obtain a number of Darbouxtransformed Dirac equations for which the zero energy solutions are exactly known.

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“…After then, the context of SUSY QM was first studied by Witten [17] and Cooper and Freedman [18]. This theory, which still attracts much attention today, has also application in optics [19] and biophysics [20]; it has a very important place in both relativistic [21] and nonrelativistic quantum mechanics [22,23]. This work points the dynamics of a massless fermion out when it is under the influence of a magnetic field.…”

Section: Introductionmentioning

confidence: 99%

The Extension of the Massless Fermion Behaviour in the Cosmic String Spacetime

Çağatay

Yeşiltaş

Aygün

2020

Advances in High Energy Physics

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In this work, we have obtained the solutions of a massless fermion which is under the external magnetic field around a cosmic string for specific three potential models using supersymmetric quantum mechanics. The constant magnetic field, energy-dependent potentials, and position-dependent mass models are investigated for the Dirac Hamiltonians, and an extension of these three potential models and their solutions is also obtained. The energy spectrum and potential graphs for each case are discussed for the α deficit angle.

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Exact energy spectrum of the generalized Dirac oscillator in an electric field

Cited by 14 publications

References 15 publications

Dirac oscillator in a uniform electric field: Path integral treatment

Dirac oscillator in a uniform electric field: Path integral treatment

Dirac systems with magnetic field and position dependent mass: Darboux transformations and equivalence with generalized Dirac oscillators

The Extension of the Massless Fermion Behaviour in the Cosmic String Spacetime

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