Generalized Dirac Oscillator Research Articles

The influence of Aharonov–Casher effect on the generalized Dirac oscillator in the cosmic string space-time

In this paper, we investigate the influence of the Aharonov–Casher (A–C) effect on the generalized Dirac oscillator containing the Coulomb-type potential function related to a relativistic neutral particle having a permanent magnetic dipole moment interacting with the external electromagnetic fields in (1 + 2)-dimensional cosmic string space-time. The eigenfunctions and energy eigenvalues of such a Dirac oscillator are derived by using the Nikiforov–Uvarov method. We indicate that implementing the scenario gives the relativistic modified exact analytical solutions. In this way, we can see that the degeneracy of the relevant relativistic energy eigenvalues is broken by depending on the Coulomb strength parameter under the influence of the curvature effect and the A–C effect.

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

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 Darboux-transformed Dirac equations for which the zero energy solutions are exactly known.

Aharonov-Bohm effect on the generalized Dirac oscillator in a cosmic dislocation space-time

In this work, we investigate the spin-half relativistic particles described by the Dirac equation on the topological defect background induced by the cosmic string and torsion with an internal magnetic field. We derive the general expression of the generalized Dirac oscillator on the topological defect background and analyze the analogue of the Aharonov-Bohm effect for the Dirac oscillator with function considered as the Cornell potential, and we explain the influence of related parameters on the energy levels of the studied system.

Generalized Dirac oscillator with κ-Poincaré algebra

In this paper, the generalized Dirac oscillator with [Formula: see text]-Poincaré algebra is structured by replacing the momentum operator p with [Formula: see text] in [Formula: see text]-deformation Dirac equation. The deformed radial equation is derived for this model. Particularly, by solving the deformed radial equation, the wave functions and energy spectra which depend on deformation parameter [Formula: see text] have been obtained for these quantum systems with [Formula: see text] being a Yukawa-type potential, inverse-square-type singular potential and central fraction power singular potential in two-dimensional space, respectively. The results show that the deformation parameter [Formula: see text] can lead to decreasing of energy levels for the above quantum systems. At the same time, the degeneracy of energy spectra has been discussed and the corresponding conditions of degeneracy have been given for each case.

A Novel Exact Solution of the 2+1-Dimensional Radial Dirac Equation for the Generalized Dirac Oscillator with the Inverse Potentials

The generalized Dirac oscillator as one of the exact solvable models in quantum mechanics was introduced in 2+1-dimensional world in this paper. What is more, the general expressions of the exact solutions for these models with the inverse cubic, quartic, quintic, and sixth power potentials in radial Dirac equation were further given by means of the Bethe ansatz method. And finally, the corresponding exact solutions in this paper were further discussed.

Generalized Dirac oscillators with position-dependent mass

We study the -dimensional generalized Dirac oscillator with a position-dependent mass. In particular, bound states with zero energy as well as non-zero energy have been obtained for suitable choices of the mass function/oscillator interaction. It has also been shown that in the presence of an electric field, bound states exist if the magnitude of the electric field does not exceed a critical value.

Generalized Dirac Oscillator in Cosmic String Space-Time

In this work, the generalized Dirac oscillator in cosmic string space-time is studied by replacing the momentum pμ with its alternative pμ+mωβfμxμ. In particular, the quantum dynamics is considered for the function fμxμ to be taken as Cornell potential, exponential-type potential, and singular potential. For Cornell potential and exponential-type potential, the corresponding radial equations can be mapped into the confluent hypergeometric equation and hypergeometric equation separately. The corresponding eigenfunctions can be represented as confluent hypergeometric function and hypergeometric function. The equations satisfied by the exact energy spectrum have been found. For singular potential, the wave function and energy eigenvalue are given exactly by power series method.

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

We study generalized (1+1)-dimensional Dirac oscillator in nonuniform electric field. It is shown that in the case of specially chosen electric field the eigenvalue equation can be casted in the form of supersymmetric quantum mechanics. It gives a possibility to find exact solution for the energy spectrum of the generalized Dirac oscillator in nonuniform electric field. Explicit examples of exact solutions are presented. We show that sufficiently large electric field destroys the bounded eigenstates.

Pseudo-Hermitian generalized Dirac oscillators

We study generalized Dirac oscillators with complex interactions in (1+1) dimensions. It is shown that for the choice of interactions considered here, the Dirac Hamiltonians are η-pseudo-Hermitian with respect to certain metric operators η. Exact solutions for the generalized Dirac oscillator for some choices of the interactions have also been obtained. It is also shown that generalized Dirac oscillators can be identified with an anti-Jaynes–Cummings-type model and by spin flipping they can also be identified with a Jaynes–Cummings-type model.

Quasi-exact solvability of Dirac?Pauli equation and generalized Dirac oscillators

In this paper we demonstrate that neutral Dirac particles in external electric fields, which are equivalent to generalized Dirac oscillators, are physical examples of quasi-exactly solvable systems. Electric field configurations permitting quasi-exact solvability of the system based on the sl (2) symmetry are discussed separately in the spherical, cylindrical, and Cartesian coordinates. Some exactly solvable field configurations are also exhibited.

Quasi-exact solvability of Dirac–Pauli equation and generalized Dirac oscillators

In this paper we demonstrate that neutral Dirac particles in external electric fields, which are equivalent to generalized Dirac oscillators, are physical examples of quasi-exactly solvable systems. Electric field configurations permitting quasi-exact solvability of the system based on the sl(2) symmetry are discussed separately in the spherical, cylindrical, and Cartesian coordinates. Some exactly solvable field configurations are also exhibited.

Bound states of the Dirac equation for a class of effective quadratic plus inversely quadratic potentials

The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm–Liouville problem, regardless the sign of the parameter of the linear potential, in sharp contrast with the Schrödinger case. The generalized Dirac oscillator already analyzed in a previous work is obtained as a particular case.