Related papers: Harmonic and Dirac oscillators in a (2+1)-dimensio…
The Dirac oscillator is a relativistic quantum system, characterized by its linearity in both position and momentum. Moreover, considering $(1{+}1)$ and $(2{+}1)$ dimensions, the system can be mapped onto the Jaynes-Cummings and…
We study a quantum model with non-isotropic two-dimensional oscillator potential but with additional quadratic interaction $x_1x_2$ with imaginary coupling constant. It is shown, that for a specific connection between coupling constant and…
We generalize the notion of harmonic conjugate functions and Hilbert transforms to higher dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These conjugate functions are in general far from being…
The one-particle three-dimensional Dirac equation with spherical symmetry is solved for the Hulthen potential. The s-wave relativistic energy spectrum and two-component spinor wavefunctions are obtained analytically. Conforming to the…
The effect of phase space general noncommutativity on producing deformed coherent squeezed states is examined. A two-dimensional noncommutative quantum system supported by a deformed mathematical structure similar to that of Hadamard…
We provide a systematic procedure to relate a three dimensional q-deformed oscillator algebra to the corresponding algebra satisfied by canonical variables describing noncommutative spaces. The large number of possible free parameters in…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
We examine the non-inertial effects of a rotating frame on a Dirac oscillator in a cosmic string space-time with non-commutative geometry in phase space. We observe that the approximate bound-state solutions are related to the biconfluent…
We consider an isotropic two dimensional harmonic oscillator with arbitrarily time-dependent mass $M(t)$ and frequency $\Omega(t)$ in an arbitrarily time-dependent magnetic field $B(t)$. We determine two commuting invariant observables (in…
The effect of the built-in supersymmetric quantum mechanical language on the spectrum of the (1+1)-Dirac equation, with position-dependent mass (PDM) and complexified Lorentz scalar interactions, is re-emphasized. The signature of the…
We study the semirelativistic Hamiltonian operator composed of the relativistic kinetic energy and a static harmonic-oscillator potential in three spatial dimensions and construct, for bound states with vanishing orbital angular momentum,…
We show that a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials has not only a spin symmetry but an U(3) symmetry and that a Dirac Hamiltonian with scalar and vector harmonic oscillator potentials equal in…
In this paper, we investigate the bound-state solutions of the noncommutative Dirac oscillator with a permanent electric dipole moment in the presence of an electromagnetic field in (2+1)-dimensions. We consider a radial magnetic field…
We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a $(2+1)$-dimensional Riemann (curved) spacetime.…
A nonlinear model of the quantum harmonic oscillator on two-dimensional spaces of constant curvature is exactly solved. This model depends of a parameter $\la$ that is related with the curvature of the space. Firstly the relation with other…
We consider the consistent deformation of the relativistic quantum mechanics introducing the noncommutativity of the space-time and preserving the Lorentz symmetry. The relativistic wave equation describing the spinning particle on…
The core concept of quantum simulation is the mapping of an inaccessible quantum system onto a controllable one by identifying analogous dynamics. We map the Dirac equation of relativistic quantum mechanics in 3+1 dimensions onto a…
In this note, we consider the Dirac operator $D$ on a Riemannian symmetric space $M$ of noncompact type. Using representation theory we show that $D$ has point spectrum iff the $\hat A$-genus of its compact dual does not vanish. In this…
The system of two-dimensional damped harmonic oscillator is revisited in the extended phase space. It is an old problem already addressed by many authors that we present here in some fresh points of view and carry on smoothly a whole…
% Doubly Special Relativity (DSR) introduces, besides the invariant speed of light $c$, an observer-independent high-energy % scale that deforms relativistic kinematics and can be implemented through modified dispersion relations or…