In this work the dynamics of a 2D Dirac oscillator in the spacetime of a magnetic cosmic string is considered. It is shown that earlier approaches to this problem have neglected a δ function contribution to the full Hamiltonian, which comes from the Zeeman interaction. The inclusion of spin effects leads to results which confirm a modified dynamics. Based on the self-adjoint extension method, we determined the most relevant physical quantities, such as energy spectrum, wave functions and the self-adjoint extension parameter by applying boundary conditions allowed by the system.

-In this work the Dirac oscillator in (2 + 1) dimensions is considered. We solve the problem in polar coordinates and discuss the dependence of the energy spectrum on the spin parameter s and angular momentum quantum number m. Contrary to earlier attempts, we show that the degeneracy of the energy spectrum can occur for all possible values of sm. In an additional analysis, we also show that an isolated bound state solution, excluded from SturmLiouville problem, exists.The Dirac oscillator, first introduced in [1] and after develop in [2], has been an usual model for studying the physical properties of physical systems in various branches of physics. In the context of theoretical contributions, the Dirac oscillator has been analyzed under different aspects such as the study of the covariance properties and FoldyWouthuysen and Cini-Touschek transformations [3], as a special case of a class of chiral solutions to the automorphism gauge field equations [4], and hidden supersymmetry produced by the interaction iM ωβr, where M is the mass, ω the frequency of the oscillator and r is the position vector, when it plays a role of anomalous magnetic interaction [5] (see also Refs. [3,6]).Recently, the one-dimensional Dirac oscillator has had its first experimental realization [7], which made the system more attractive from the point of view of applications. The Dirac oscillator in (2 + 1) dimensions, when the third spatial coordinate is absent, has also been studied in Refs. [8][9][10]. Additionally, this system was proposed in [11] to describe some electronic properties of monolayer an bylayer graphene. For a detailed approach of the Dirac oscillator see the Refs. [12,13].In this Letter, we address the Dirac oscillator in (2 + 1) dimensions. In [10], it was argued that the energy eigenvalues are degenerated only for negative values of k ϑ s, where k ϑ represents the angular momentum quantum number and s the spin projection parameter. This result, however, is not correct, as properly shown in this work. Additionally, an isolated bound state solution for the Dirac oscillator in (2 + 1) is worked out.We begin by writing the Dirac equation in (2 + 1) dimensions ( = c = 1)where p = (p x , p y ) is the momentum operator and ψ is a two-component spinor. The Dirac oscillator is obtained through the following nonminimal substitution [2]:where r = (x, y) is the position vector and ω stands for the Dirac oscillator frequency. Thus, the relevant equation isIn three dimensions the γ matrices are conveniently defined in terms of the Pauli matrices [14]where s is twice the spin value, with s = +1 for spin "up" and s = −1 for spin "down". In this manner, eq. (3) can be written aswhere π j = p j − iM ωσ z r j .p-1

A two dimensional electron gas on a cylindrical surface with a screw dislocation is considered. More precisely, we investigate how both the geometry and the deformed potential due to a lattice distortion affect the Landau levels of such system. The case showing the deformed potential can be thought in the context of 3D common semiconductors where the electrons are confined on a cylindrical shell. We will show that important quantitative differences exist due to this lattice distortion. For instance, the effective cyclotron frequency is diminished by the deformed potential, which in turn enhances the Hall conductivity

In this paper we investigate the bound state problem of nonrelativistic quantum particles on a conical surface. This kind of surface appears as a topological defect in ordinary semiconductors as well as in graphene sheets. Specifically, we compare and discuss the results stemming from two different approaches. In the first one, it is assumed that the charge carriers are bound to the surface by a constraining potential, while the second one is based on the Klein-Gordon type equation on surfaces, without the constraining potential. The main difference between both theories is the presence/absence of a potential which contains the mean curvature of a given surface. This fact changes the dependence of the bound states on the angular momentum l. Moreover, there are bound states that are absent in the Klein-Gordon theory, which instead appear in the Schrödinger one. C 2012 American Institute of Physics.

In this paper, we investigate the influence of a screw dislocation on the energy levels and the wavefunctions of an electron confined in a two-dimensional pseudoharmonic quantum dot under the influence of an external magnetic field inside a dot and Aharonov-Bohm field inside a pseudodot. The exact solutions for energy eigenvalues and wavefunctions are computed as functions of applied uniform magnetic field strength, Aharonov-Bohm flux, magnetic quantum number and the parameter characterizing the screw dislocation, the Burgers vector. We investigate the modifications due to the screw dislocation on the light interband absorption coefficient and absorption threshold frequency. Two scenarios are possible, depending on if singular effects either manifest or not. We found that as the Burgers vector increases, the curves of frequency are pushed up towards of the growth of it. One interesting aspect which we have observed is that the Aharonov-Bohm flux can be tuned in order to cancel the screw effect of the model.