scholarly journals The massless Dirac–Weyl equation with deformed extended complex potentials

2018 ◽  
Vol 96 (7) ◽  
pp. 770-773
Author(s):  
Özlem Yeşiltaş ◽  
Bengü Çag̃atay
Keyword(s):  
Energy Spectrum ◽  
Scalar Potential ◽  
Fermi Velocity ◽  
Effective Hamiltonian ◽  
Velocity Function ◽  
Lorentz Scalar ◽  
Klein Gordon ◽  
Extended Complex ◽  
Weyl Equation ◽  
Dirac Hamiltonian

Basically (2 + 1)-dimensional Dirac equation with real deformed Lorentz scalar potential is investigated in this study. The position-dependent Fermi velocity function transforms Dirac Hamiltonian into a Klein–Gordon-like effective Hamiltonian system. The complex Hamiltonian and its real energy spectrum and eigenvectors are obtained analytically. Moreover, the Lie algebraic analysis is also performed.

scholarly journals DYNAMICAL SYMMETRIES OF DIRAC HAMILTONIAN

2012 ◽  
Vol 27 (06) ◽  
pp. 1230004
Author(s):  
RIAZUDDIN
Keyword(s):  
Angular Momentum ◽  
Energy Spectrum ◽  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Scalar Potential ◽  
Dynamical Symmetries ◽  
Lorentz Scalar ◽  
Relativistic Hydrogen ◽  
Relativistic Hydrogen Atom ◽  
Dirac Hamiltonian

Several dynamical symmetries of the Dirac Hamiltonian are reviewed and the conditions under which such symmetries hold are considered. These include relativistic spin and orbital angular momentum symmetries, SO (4)× SU σ(2) symmetry for generalized relativistic hydrogen atom that includes an extra Lorentz scalar potential, SU (3)× SU σ(2) symmetry for the relativistic simple harmonic oscillator. The energy spectrum in each case is calculated from group-theoretic considerations.

scholarly journals Bound state solutions of the Klein–Gordon equation with energy-dependent potentials

2020 ◽  
pp. 2150016
Author(s):  
B. C. Lütfüoğlu ◽  
A. N. Ikot ◽  
M. Karakoc ◽  
G. T. Osobonye ◽  
A. T. Ngiangia ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Gordon Equation ◽  
Scalar Potential ◽  
Bound State ◽  
Asymptotic Iteration Method ◽  
Equal Sign ◽  
Tuning Parameters ◽  
Klein Gordon ◽  
Energy Dependent ◽  
Klein Gordon Equation

In this paper, we investigate the exact bound state solution of the Klein–Gordon equation for an energy-dependent Coulomb-like vector plus scalar potential energies. To the best of our knowledge, this problem is examined in literature with a constant and position dependent mass functions. As a novelty, we assume a mass-function that depends on energy and position and revisit the problem with the following cases: First, we examine the case where the mixed vector and scalar potential energy possess equal magnitude and equal sign as well as an opposite sign. Then, we study pure scalar and pure vector cases. In each case, we derive an analytic expression of the energy spectrum by employing the asymptotic iteration method. We obtain a nontrivial relation among the tuning parameters which lead the examined problem to a constant mass one. Finally, we calculate the energy spectrum by the Secant method and show that the corresponding unnormalized wave functions satisfy the boundary conditions. We conclude the paper with a comparison of the calculated energy spectra versus tuning parameters.

Dirac particle in electric field with confining scalar potential on (anti)-de Sitter background

2018 ◽  
Vol 33 (34) ◽  
pp. 1850202 ◽  
Author(s):  
N. Messai ◽  
B. Hamil ◽  
A. Hafdallah
Keyword(s):  
Energy Spectrum ◽  
Dirac Equation ◽  
Electric Field ◽  
Scalar Potential ◽  
Dirac Particle ◽  
Wave Functions ◽  
De Sitter ◽  
Sitter Background ◽  
Position Representation

In this paper, we study the (1 + 1)-dimensional Dirac equation in the presence of electric field and scalar linear potentials on (anti)-de Sitter background. Using the position representation, the energy spectrum and the corresponding wave functions are exactly obtained.

scholarly journals Bound State Solutions of Three-Dimensional Klein-Gordon Equation for Two Model Potentials by NU Method

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
N. Tazimi ◽  
A. Ghasempour
Keyword(s):  
Gordon Equation ◽  
Scalar Potential ◽  
Laguerre Polynomials ◽  
Three Dimensional ◽  
Bound State ◽  
Molecular Systems ◽  
Klein Gordon ◽  
Linear Differential ◽  
Nu Method ◽  
Klein Gordon Equation

In this study, we investigate the relativistic Klein-Gordon equation analytically for the Deng-Fan potential and Hulthen plus Eckart potential under the equal vector and scalar potential conditions. Accordingly, we obtain the energy eigenvalues of the molecular systems in different states as well as the normalized wave function in terms of the generalized Laguerre polynomials function through the NU method, which is an effective method for the exact solution of second-order linear differential equations.

scholarly journals Klein–Gordon particle near RN black hole, generalized sl(2) algebra and harmonic oscillator energy

2019 ◽  
Vol 34 (31) ◽  
pp. 1950196
Author(s):  
J. Sadeghi ◽  
M. R. Alipour
Keyword(s):  
Differential Equation ◽  
Information Theory ◽  
Black Hole ◽  
Energy Spectrum ◽  
Harmonic Oscillator ◽  
Three Dimensional ◽  
The Other ◽  
Thermodynamical Properties ◽  
Heun Functions ◽  
Klein Gordon

In this paper, we consider Klein–Gordon particle near Reissner–Nordström black hole. The symmetry of such a background led us to compare the corresponding Laplace equation with the generalized Heun functions. Such relations help us achieve the generalized [Formula: see text] algebra and some suitable results for describing the above-mentioned symmetry. On the other hand, in case of [Formula: see text], which is near the proximity black hole, we obtain the energy spectrum. When we compare the equation of RN background with Laguerre differential equation, we show that the obtained energy spectrum is same as the three-dimensional harmonic oscillator. So, finally we take advantage of harmonic oscillator energy and make suitable partition function. Such function help us to obtain all thermodynamical properties of black hole. Also, the structure of obtained entropy lead us to have some bit and information theory in the RN black hole.

THE ASYMPTOTIC ITERATION METHOD FOR DIRAC AND KLEIN–GORDON EQUATIONS WITH A LINEAR SCALAR POTENTIAL

2006 ◽  
Vol 21 (19n20) ◽  
pp. 4127-4135 ◽  
Author(s):  
T. BARAKAT
Keyword(s):  
Iteration Method ◽  
Bound States ◽  
Scalar Potential ◽  
Asymptotic Iteration Method ◽  
Klein Gordon ◽  
Linear Scalar

The asymptotic iteration method is used for Dirac and Klein–Gordon equations with a linear scalar potential to obtain the relativistic eigenenergies. A parameter, ς = 0, 1, is introduced in such a way that one can obtain Klein–Gordon bound states from Dirac bound states. It is shown that this method asymptotically gives accurate results for both Dirac and Klein–Gordon equations.

scholarly journals Relativistic scalar particle subject to a confining potential and Lorentz symmetry breaking effects in the cosmic string space–time

2016 ◽  
Vol 31 (07) ◽  
pp. 1650026 ◽  
Author(s):  
H. Belich ◽  
K. Bakke
Keyword(s):  
Symmetry Breaking ◽  
Cosmic String ◽  
Gordon Equation ◽  
Scalar Potential ◽  
Scalar Particle ◽  
Lorentz Symmetry ◽  
Space Time ◽  
Klein Gordon ◽  
Lorentz Symmetry Breaking ◽  
Klein Gordon Equation

The behavior of a relativistic scalar particle subject to a scalar potential under the effects of the violation of the Lorentz symmetry in the cosmic string space–time is discussed. It is considered two possible scenarios of the Lorentz symmetry breaking in the CPT-even gauge sector of the Standard Model Extension defined by a tensor [Formula: see text]. Then, by introducing a scalar potential as a modification of the mass term of the Klein–Gordon equation, it is shown that the Klein–Gordon equation in the cosmic string space–time is modified by the effects of the Lorentz symmetry violation backgrounds and bound state solution to the Klein–Gordon equation can be obtained.

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.

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