SOLUTION OF THE DIRAC EQUATION WITH POSITION-DEPENDENT MASS IN A COULOMB AND SCALAR FIELDS IN A CONICAL SPACETIME

2013 ◽  
Vol 28 (31) ◽  
pp. 1350137 ◽  
Author(s):  
GEUSA DE A. MARQUES ◽  
V. B. BEZERRA ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Cosmic String ◽  
Relativistic Particle ◽  
Energy Levels ◽  
Scalar Potential ◽  
Scalar Fields ◽  
The Self ◽  
Dependent Mass ◽  
Scalar Potentials ◽  
Position Dependent Mass

We consider the problem of a relativistic particle with position-dependent mass in the presence of a Coulomb and a scalar potentials in the background spacetime generated by a cosmic string. The scalar potential arises from the self-interaction potential which is induced by the conical geometry of the spacetime under consideration. We find the solution of the corresponding Dirac equation and determine the energy spectrum of the particle. The behavior of the energy levels on the parameters associated with the presence of the cosmic string and with the fact that the mass of the particle depends on its position is also analyzed.

Klein–Gordon oscillator with position-dependent mass in the rotating cosmic string spacetime

2018 ◽  
Vol 33 (04) ◽  
pp. 1850025 ◽  
Author(s):  
Bing-Qian Wang ◽  
Zheng-Wen Long ◽  
Chao-Yun Long ◽  
Shu-Rui Wu
Keyword(s):  
Magnetic Field ◽  
Cosmic String ◽  
Energy Levels ◽  
Homogeneous Magnetic Field ◽  
Spinless Particle ◽  
Klein Gordon ◽  
Coulomb Type ◽  
Dependent Mass ◽  
String Background ◽  
Position Dependent Mass

A spinless particle coupled covariantly to a uniform magnetic field parallel to the string in the background of the rotating cosmic string is studied. The energy levels of the electrically charged particle subject to the Klein–Gordon oscillator are analyzed. Afterwards, we consider the case of the position-dependent mass and show how these energy levels depend on the parameters in the problem. Remarkably, it shows that for the special case, the Klein–Gordon oscillator coupled covariantly to a homogeneous magnetic field with the position-dependent mass in the rotating cosmic string background has the similar behaviors to the Klein–Gordon equation with a Coulomb-type configuration in a rotating cosmic string background in the presence of an external magnetic field.

Ansatz approach solution of the Duffin–Kemmer–Petiau equation for spin-1 particles with position-dependent mass in the presence of Kratzer-type potential

2014 ◽  
Vol 92 (12) ◽  
pp. 1565-1569 ◽  
Author(s):  
M.K. Bahar ◽  
F. Yasuk
Keyword(s):  
Wave Function ◽  
Scalar Potential ◽  
Energy Eigenvalues ◽  
Relativistic Spin ◽  
Ansatz Approach ◽  
Dependent Mass ◽  
Type Potential ◽  
Position Dependent Mass

The relativistic Duffin–Kemmer–Petiau equation for relativistic spin-1 particles with position-dependent mass in the presence of a vector Kratzer-type potential and the absence of a scalar potential is studied analytically. The energy eigenvalues and corresponding eigenfunctions are obtained using the wave function ansatz approach.

scholarly journals Bound state of solution of Dirac-Coulomb problem with spatially dependent mass

Open Physics ◽  
2014 ◽  
Vol 12 (4) ◽  
Author(s):  
Eser Olğar ◽  
Hayder Dhahir ◽  
Haydar Mutaf
Keyword(s):  
Dirac Equation ◽  
Coulomb Potential ◽  
Mass Function ◽  
Bound State ◽  
Asymptotic Iteration Method ◽  
Bound State Solution ◽  
Function Generator ◽  
Dependent Mass ◽  
And Function ◽  
Position Dependent Mass

AbstractThe bound state solution of Coulomb Potential in the Dirac equation is calculated for a position dependent mass function M(r) within the framework of the asymptotic iteration method (AIM). The eigenfunctions are derived in terms of hypergeometric function and function generator equations of AIM.

EXACT SOLUTIONS OF DIRAC EQUATION FOR A NEW SPHERICALLY ASYMMETRICAL SINGULAR OSCILLATOR

2010 ◽  
Vol 25 (33) ◽  
pp. 2849-2857 ◽  
Author(s):  
GUO-HUA SUN ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Vector Potential ◽  
State Energy ◽  
Energy Levels ◽  
Scalar Potential ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Exact Bound ◽  
Spinor Wave

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of scalar and vector spherically asymmetrical singular oscillators. This is done provided that the vector potential is equal to the scalar potential. The spinor wave functions and bound state energy levels are presented. The case V(r) = -S(r) is also considered.

scholarly journals Self-Adjoint Extension Approach to Motion of Spin-1/2 Particle in the Presence of External Magnetic Fields in the Spinning Cosmic String Spacetime

Universe ◽  
2020 ◽  
Vol 6 (11) ◽  
pp. 203
Author(s):  
Márcio M. Cunha ◽  
Edilberto O. Silva
Keyword(s):  
Energy Spectrum ◽  
Dirac Equation ◽  
Magnetic Fields ◽  
Cosmic String ◽  
Relativistic Quantum ◽  
Wave Functions ◽  
The Self ◽  
Extension Method ◽  
Adjoint Extension ◽  
Quantum Motion

In this work, we study the relativistic quantum motion of an electron in the presence of external magnetic fields in the spinning cosmic string spacetime. The approach takes into account the terms that explicitly depend on the particle spin in the Dirac equation. The inclusion of the spin element in the solution of the problem reveals that the energy spectrum is modified. We determine the energies and wave functions using the self-adjoint extension method. The technique used is based on boundary conditions allowed by the system. We investigate the profiles of the energies found. We also investigate some particular cases for the energies and compare them with the results in the literature.

scholarly journals SOME ASPECTS OF SPHERICAL SYMMETRIC EXTREMAL DYONIC BLACK HOLES IN 4D N = 1 SUPERGRAVITY

2013 ◽  
Vol 28 (18) ◽  
pp. 1350084 ◽  
Author(s):  
BOBBY E. GUNARA ◽  
FREDDY P. ZEN ◽  
FIKI T. AKBAR ◽  
AGUS SUROSO ◽  
ARIANTO
Keyword(s):  
Black Hole ◽  
Scalar Potential ◽  
Local Existence ◽  
Scalar Fields ◽  
Asymptotic Region ◽  
De Sitter ◽  
Complex Scalar ◽  
Symmetric Black Hole ◽  
Scalar Potentials ◽  
Nonzero Scalar

In this paper, we study several aspects of extremal spherical symmetric black hole solutions of four-dimensional N = 1 supergravity coupled to vector and chiral multiplets with the scalar potential turned on. In the asymptotic region, the complex scalars are fixed and regular which can be viewed as the critical points of the black hole and the scalar potentials with vanishing scalar charges. It follows that the asymptotic geometries are of a constant and nonzero scalar curvature which are generally not Einstein. These spaces could also correspond to the near horizon geometries which are the product spaces of a two anti-de Sitter surface and the two sphere if the value of the scalars in both regions coincide. In addition, we prove the local existence of nontrivial radius dependent complex scalar fields which interpolate between the horizon and the asymptotic region. We finally give some simple ℂn-models with both linear superpotential and gauge couplings.

scholarly journals Dirac equation with complex potentials

2014 ◽  
Vol 29 (40) ◽  
pp. 1450210 ◽  
Author(s):  
C.-L. Ho ◽  
P. Roy
Keyword(s):  
Dirac Equation ◽  
Scalar Potential ◽  
Complex Potentials ◽  
Zero Energy ◽  
Complex Scalar ◽  
Exact Analytical Solutions ◽  
Exactly Solvable ◽  
Lorentz Scalar ◽  
Scalar Potentials ◽  
Energy Dependent

We study (2+1)-dimensional Dirac equation with complex scalar and Lorentz scalar potentials. It is shown that the Dirac equation admits exact analytical solutions with real eigenvalues for certain complex potentials while for another class of potentials zero energy solutions can be obtained analytically. For the scalar potential cases, it has also been shown that the effective Schrödinger-like equations resulting from decoupling the spinor components can be interpreted as exactly solvable energy-dependent Schrödinger equations.

The study of a spinless relativistic particle in the spinning cosmic string space–time

2017 ◽  
Vol 95 (4) ◽  
pp. 331-335 ◽  
Author(s):  
Zhi Wang ◽  
Zheng-wen Long ◽  
Chao-yun Long ◽  
Bing-qian Wang
Keyword(s):  
Cosmic String ◽  
Gordon Equation ◽  
Relativistic Particle ◽  
Energy Levels ◽  
Space Time ◽  
Rotational Parameter ◽  
Cylindrically Symmetric ◽  
Background Space ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this paper we analyze a spinless relativistic particle depicted by the Klein–Gordon equation in the spinning cosmic string space–time. The solutions of the Klein–Gordon equation in the presence of a uniform magnetic field and the Klein–Gordon equation with two common cylindrically symmetric scalar potentials under the background space–time are presented; the energy spectrum and the corresponding wave functions of these systems are obtained by using the functional analysis method. It is shown that the energy levels of the considered physical systems depend explicitly on the angular deficit α and the rotational parameter a, which characterize the global structure of the metric in the space–time of the spinning cosmic string.

scholarly journals Position-dependent mass Dirac equation and local Fermi velocity

2021 ◽  
Author(s):  
Rahul Ghosh
Keyword(s):  
Dirac Equation ◽  
Free Particle ◽  
Quadratic Functional ◽  
Fermi Velocity ◽  
New Approach ◽  
Coupled Equations ◽  
The One ◽  
Dependent Mass ◽  
Local Variable ◽  
Position Dependent Mass

Abstract We present a new approach to study the one-dimensional Dirac equation in the background of a position-dependent mass m. Taking the Fermi velocity vf to be a local variable, we explore the resulting structure of the coupled equations and arrive at an interesting constraint of m turning out to be the inverse square of vf. We address several solvable systems that include the free particle, shifted harmonic oscillator, Coulomb and nonpolynomial potentials. In particular, in the supersymmetric quantum mechanics context, the upper partner of the effective potential yields a new form for an inverse quadratic functional choice of the Fermi velocity.

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