EXACT SOLUTIONS OF DIRAC EQUATION WITH HARTMANN POTENTIAL BY NIKIFOROV–UVAROV METHOD

2010 ◽  
Vol 19 (11) ◽  
pp. 2189-2197 ◽  
Author(s):  
M. HAMZAVI ◽  
H. HASSANABADI ◽  
A. A. RAJABI
Keyword(s):  
Dirac Equation ◽  
State Energy ◽  
Bound State ◽  
Energy Eigenvalues ◽  
Dirac Particles ◽  
Uvarov Method ◽  
Spinor Wave ◽  
Polar Parts ◽  
Component Spinor ◽  
Hartmann Potential

We investigate the exact solution of the Dirac equation for the Hartmann potential. The radial and polar parts of the Dirac equation are solved by Nikiforov–Uvarov method. The bound state energy eigenvalues and the corresponding two-component spinor wave functions of the Dirac particles are obtained.

scholarly journals Pseudo-spin Symmetry in Dirac-Four-Parameter Diatomic Problem Coupled with a Coulomb-like Tensor potential

BIBECHANA ◽  
2012 ◽  
Vol 8 ◽  
pp. 23-30
Author(s):  
Mahdi Eshghi
Keyword(s):  
Energy Spectrum ◽  
Dirac Equation ◽  
State Energy ◽  
Spin Symmetry ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Tensor Potential ◽  
Uvarov Method ◽  
Spinor Wave

In this work, we use the parametric generalization of the Nikiforov-Uvarov method to obtain the relativistic bound state energy spectrum and the corresponding spinor wave-functions for four-parameter diatomic potential coupled with a Coulomb-like tensor under the condition of the pseudo-spin symmetry. Also, some numerical results have given.Keywords: Dirac equation; four-parameter diatomic potential; Coulomb-like tensorDOI: http://dx.doi.org/10.3126/bibechana.v8i0.4879BIBECHANA 8 (2012) 23-30

Relativistic symmetries of fermions in the background of the inversely quadratic Yukawa potential with Yukawa potential as a tensor

2014 ◽  
Vol 92 (1) ◽  
pp. 51-58
Author(s):  
Majid Hamzavi ◽  
Sameer M. Ikhdair
Keyword(s):  
Yukawa Potential ◽  
Bound State ◽  
Arbitrary Spin ◽  
Tensor Interaction ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Yukawa Tensor Interaction ◽  
Uvarov Method ◽  
Spinor Wave ◽  
Component Spinor

In the presence of spin and pseudo-spin symmetries, we obtain approximate analytical bound state solutions to the Dirac equation with scalar–vector inverse quadratic Yukawa potential including a Yukawa tensor interaction for any arbitrary spin–orbit quantum number, κ. The energy eigenvalues and their corresponding two-component spinor wave functions are obtained in closed form using the parametric Nikiforov–Uvarov method. It is noticed that the tensor interaction removes the degeneracy in the spin and p-spin doublets. Some numerical results are obtained for the lowest energy states within spin and pseudo-spin symmetries.

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 Pseudospin and Spin Symmetric Solutions of the Dirac Equation: Hellmann Potential,Wei–Hua Potential, Varshni Potential

2014 ◽  
Vol 69 (3-4) ◽  
pp. 163-172 ◽  
Author(s):  
Altuğ Arda ◽  
Ramazan Sever
Keyword(s):  
Dirac Equation ◽  
Analytical Solutions ◽  
Energy Eigenvalue ◽  
Wave Functions ◽  
K Value ◽  
Energy Eigenvalues ◽  
Approximate Analytical Solutions ◽  
Hellmann Potential ◽  
Uvarov Method ◽  
Spinor Wave

Approximate analytical solutions of the Dirac equation are obtained for the Hellmann potential, the Wei-Hua potential, and the Varshni potential with any k-value for the cases having the Dirac equation pseudospin and spin symmetries. Closed forms of the energy eigenvalue equations and the spinor wave functions are obtained by using the Nikiforov-Uvarov method and some tables are given to see the dependence of the energy eigenvalues on different quantum number pairs (n;κ).

scholarly journals Analytical solution of energy eigen value, eigen function and angular wave function of Dirac equation with Rosen Morse plus Rosen Morse potential in terms of Romanovski polynomials for exact spin symmetry

2017 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Ihtiari Prasetyaningrum ◽  
C Cari ◽  
A Suparmi
Keyword(s):  
Dirac Equation ◽  
Morse Potential ◽  
State Energy ◽  
Spin Symmetry ◽  
Bound State ◽  
Bound State Energy ◽  
Eigenvalues And Eigenfunctions ◽  
Energy Eigenvalues ◽  
Eigen Value ◽  
Energy Eigenvalues And Eigenfunctions

<p class="Abstract">The energy eigenvalues and eigenfunctions of Dirac equation for Rosen Morse plus Rosen Morse potential are investigated numerically in terms of finite Romanovsky Polynomial. The bound state energy eigenvalues are given in a closed form and corresponding eigenfunctions are obtained in terms of Romanovski polynomials. The energi eigen value is solved by numerical method with Matlab 2011.</p>

SOLUTIONS OF THE SCHRODINGER EQUATION WITH INVERSELY QUADRATIC YUKAWA PLUS WOODS-SAXON POTENTIAL USING NIKIFOROV-UVAROV METHOD

2015 ◽  
Vol 8 (2) ◽  
pp. 2094-2098
Author(s):  
Benedict Ita ◽  
A. I. Ikeuba ◽  
O. Obinna
Keyword(s):  
State Energy ◽  
Jacobi Polynomials ◽  
Bound State ◽  
Negative Energy ◽  
Saxon Potential ◽  
Energy Eigenvalues ◽  
Eigen Values ◽  
Uvarov Method ◽  
Special Case ◽  
Nu Method

The solutions of the SchrÓ§dinger equation with inversely quadratic Yukawa plus Woods-Saxon potential (IQYWSP) have been presented using the parametric Nikiforov-Uvarov (NU) method. The bound state energy eigenvalues and the corresponding un-normalized eigen functions are obtained in terms of Jacobi polynomials. Also, a special case of the potential has been considered and its energy eigen values obtained. The result of the work could be applied to molecules moving under the influence of IQYWSP potential as negative energy eigenvalues obtained indicate a bound state system.

Analytical solution of energy eigen value, eigen function and angular wave function of Dirac equation with Rosen Morse plus Rosen Morse potential in terms of Romanovski polynomials for exact spin symmetry

2017 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Ihtiari Prasetyaningrum ◽  
C Cari ◽  
A Suparmi
Keyword(s):  
Dirac Equation ◽  
Morse Potential ◽  
State Energy ◽  
Spin Symmetry ◽  
Bound State ◽  
Bound State Energy ◽  
Eigenvalues And Eigenfunctions ◽  
Energy Eigenvalues ◽  
Eigen Value ◽  
Energy Eigenvalues And Eigenfunctions

<p class="Abstract">The energy eigenvalues and eigenfunctions of Dirac equation for Rosen Morse plus Rosen Morse potential are investigated numerically in terms of finite Romanovsky Polynomial. The bound state energy eigenvalues are given in a closed form and corresponding eigenfunctions are obtained in terms of Romanovski polynomials. The energi eigen value is solved by numerical method with Matlab 2011.</p>

scholarly journals ANALYTICAL SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH THE WOODS–SAXON POTENTIAL FOR ARBITRARY l STATE

2009 ◽  
Vol 18 (03) ◽  
pp. 631-641 ◽  
Author(s):  
V. H. BADALOV ◽  
H. I. AHMADOV ◽  
A. I. AHMADOV
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
State Energy ◽  
Bound State ◽  
Saxon Potential ◽  
Energy Eigenvalues ◽  
Quantum Numbers ◽  
Radial Schrödinger Equation ◽  
Uvarov Method ◽  
Pekeris Approximation

In this work, the analytical solution of the radial Schrödinger equation for the Woods–Saxon potential is presented. In our calculations, we have applied the Nikiforov–Uvarov method by using the Pekeris approximation to the centrifugal potential for arbitrary l states. The bound state energy eigenvalues and corresponding eigenfunctions are obtained for various values of n and l quantum numbers.

Simple way to extract solutions and features of the Dirac equation for a noncentral potentials

2016 ◽  
Vol 30 (07) ◽  
pp. 1650089
Author(s):  
T. Barakat ◽  
M. Sebawe Abdalla
Keyword(s):  
Differential Equation ◽  
Dirac Equation ◽  
Wave Equations ◽  
Order Differential Equation ◽  
Similarity Transformation ◽  
Bound State ◽  
Exact Formula ◽  
Exact Bound ◽  
Polar Parts ◽  
Hartmann Potential

The main purpose of the present study is to explore the classes of the Schrödinger-like wave equations derived from Dirac equation, for which the similarity transformation and asymptotic iteration algorithms can assist in generating second-order differential equation that admit general exact solutions in the presence of nonsymmetrical potential terms. For illustration purposes, we extract the exact bound-state solutions of the Dirac equation with the noncentral Hartmann potential for the cases of exact [Formula: see text] spin and pseudospin symmetries. Also, we have shown that both Dirac-radial and Dirac-polar parts are sensitive to the variation of the involved parameters.

EXACT SOLUTION OF DIRAC EQUATION FOR MIE-TYPE POTENTIAL BY USING THE NIKIFOROV–UVAROV METHOD UNDER THE PSEUDOSPIN AND SPIN SYMMETRY LIMIT

2010 ◽  
Vol 25 (28) ◽  
pp. 2447-2456 ◽  
Author(s):  
M. HAMZAVI ◽  
H. HASSANABADI ◽  
A. A. RAJABI
Keyword(s):  
Dirac Equation ◽  
Spin Symmetry ◽  
Wave Functions ◽  
Spin Orbit Coupling ◽  
Coupling Term ◽  
Energy Eigenvalues ◽  
Dirac Particles ◽  
Spin Symmetry Limit ◽  
Uvarov Method ◽  
Type Potential

Dirac equation is solved for Mie-type potential. The energy spectra and the corresponding wave functions are investigated with pseudospin and spin symmetry. The Nikiforov–Uvarov method is used to obtain an analytical solution of the Dirac equation and closed forms of energy eigenvalues are obtained for any spin-orbit coupling term κ. We also present some numerical results of Dirac particles for the well-known Kratzer–Fues and modified Kratzer potentials which are Mie-type potential.

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