SPIN AND PSEUDOSPIN SYMMETRIES IN RELATIVISTIC TRIGONOMETRIC PÖSCHL–TELLER POTENTIAL WITH CENTRIFUGAL BARRIER

2012 ◽  
Vol 21 (12) ◽  
pp. 1250097 ◽  
Author(s):  
M. HAMZAVI ◽  
S. M. IKHDAIR ◽  
K.-E. THYLWE
Keyword(s):  
State Energy ◽  
Bound State ◽  
Arbitrary Spin ◽  
Nonrelativistic Limit ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Centrifugal Barrier ◽  
Energy Eigenvalues ◽  
Approximate Analytical Solutions ◽  
Component Wave

Approximate analytical solutions of the Dirac equation with the trigonometric Pöschl–Teller (tPT) potential are obtained for arbitrary spin-orbit quantum number κ using an approximation scheme to deal with the spin-orbit coupling terms κ(κ±1)r-2. In the presence of exact spin and pseudo-spin (p-spin) symmetric limitation, the bound state energy eigenvalues and the corresponding two-component wave functions of the Dirac particle moving in the field of attractive and repulsive tPT potential are obtained using the parametric generalization of the Nikiforov–Uvarov (NU) method. The case of nonrelativistic limit is studied too.

scholarly journals Generalized Nuclear Woods-Saxon Potential under Relativistic Spin Symmetry Limit

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
M. Hamzavi ◽  
A. A. Rajabi
Keyword(s):  
Spin Symmetry ◽  
Arbitrary Spin ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Saxon Potential ◽  
Symmetry Limit ◽  
Energy Eigenvalues ◽  
Spin Symmetry Limit ◽  
Pekeris Approximation ◽  
Coupling Number

By using the Pekeris approximation, we present solutions of the Dirac equation with the generalized Woods-Saxon potential with arbitrary spin-orbit coupling number under spin symmetry limit. We obtain energy eigenvalues and corresponding eigenfunctions in closed forms. Some numerical results are given too.

scholarly journals Hulthén and Coulomb-Like Potentials as a Tensor Interaction within the Relativistic Symmetries of the Manning-Rosen Potential

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Hadi Tokmehdashi ◽  
Ali Akbar Rajabi ◽  
Majid Hamzavi
Keyword(s):  
Spin Symmetry ◽  
Bound State ◽  
Arbitrary Spin ◽  
Tensor Interaction ◽  
Spin Orbit ◽  
Energy Eigenvalues ◽  
Dirac Particles ◽  
Two Component ◽  
Rosen Potential ◽  
Nu Method

The bound-state solutions of the Dirac equation for the Manning-Rosen potential are presented approximately for arbitrary spin-orbit quantum numberκwith the Hulthén and Coulomb-like potentials as a tensor interaction. The generalized parametric Nikiforov-Uvarov (NU) method is used to obtain energy eigenvalues and corresponding two-component spinors of the two Dirac particles and these are obtained in the closed form by using the framework of the spin symmetry and p-spin symmetry concept. We have also shown that tensor interaction removes degeneracies between spin and p-spin doublets. Some numerical results are also given.

Arbitrary l-state solutions of the Schrödinger equation for the Eckart potential with an improved approximation of the centrifugal term

Open Physics ◽  
2011 ◽  
Vol 9 (6) ◽  
Author(s):  
Jerzy Stanek
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
State Energy ◽  
Bound State ◽  
Centrifugal Term ◽  
Energy Eigenvalues ◽  
Eckart Potential ◽  
Quantum Numbers ◽  
Approximate Analytical Solutions ◽  
Screening Parameter

AbstractApplying an improved approximation scheme to the centrifugal term, the approximate analytical solutions of the Schrödinger equation for the Eckart potential are presented. Bound state energy eigenvalues and the corresponding eigenfunctions are obtained in closed forms for the arbitrary radial and angular momentum quantum numbers, and different values of the screening parameter. The results are compared with those obtained by the other approximate and numerical methods. It is shown that the present method is systematic, more efficient and accurate.

Effect of the velocity-dependent potentials on the energy eigenvalues of the Morse potential

Open Physics ◽  
2012 ◽  
Vol 10 (4) ◽  
Author(s):  
Asim Soylu ◽  
Orhan Bayrak ◽  
Ismail Boztosun
Keyword(s):  
Morse Potential ◽  
State Energy ◽  
Bound State ◽  
Quantum States ◽  
Bound State Energy ◽  
Energy Eigenvalues ◽  
Dependent Term ◽  
Oscillator Type ◽  
Dependent Potential ◽  
Pekeris Approximation

AbstractWe investigate the effect of the isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Morse potential for any quantum states. When the velocity-dependent term is used as a constant parameter, ρ(r) = ρ 0, the energy eigenvalues can be obtained analytically by using the Pekeris approximation. When the velocity-dependent term is considered as an harmonic oscillator type, ρ(r) = ρ 0 r 2, we show how to obtain the energy eigenvalues of the Morse potential without any approximation for any n and ℓ quantum states by using numerical calculations. The calculations have been performed for different energy eigenvalues and different numerical values of ρ 0, in order to show the contribution of the velocity-dependent potential on the energy eigenvalues of the Morse potential.

scholarly journals ANY l-STATE ANALYTICAL SOLUTIONS OF THE KLEIN–GORDON EQUATION FOR THE WOODS–SAXON POTENTIAL

2010 ◽  
Vol 19 (07) ◽  
pp. 1463-1475 ◽  
Author(s):  
V. H. BADALOV ◽  
H. I. AHMADOV ◽  
S. V. BADALOV
Keyword(s):  
State Energy ◽  
Gordon Equation ◽  
Bound State ◽  
Nonrelativistic Limit ◽  
Saxon Potential ◽  
Bound State Energy ◽  
Klein Gordon ◽  
Uvarov Method ◽  
Pekeris Approximation ◽  
Klein Gordon Equation

The radial part of the Klein–Gordon equation for the Woods–Saxon potential is solved. In our calculations, we have applied the Nikiforov–Uvarov method by using the Pekeris approximation to the centrifugal potential for any l-states. The exact bound state energy eigenvalues and the corresponding eigenfunctions are obtained on the various values of the quantum numbers n and l. The nonrelativistic limit of the bound state energy spectrum was also found.

scholarly journals EXACT SOLUTION OF THE SCHRÖDINGER EQUATION FOR THE MODIFIED KRATZER'S MOLECULAR POTENTIAL WITH POSITION-DEPENDENT MASS

2008 ◽  
Vol 17 (07) ◽  
pp. 1327-1334 ◽  
Author(s):  
RAMAZÀN SEVER ◽  
CEVDET TEZCAN
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
State Energy ◽  
Bound State ◽  
Bound State Energy ◽  
Energy Eigenvalues ◽  
Molecular Potential ◽  
Dependent Mass ◽  
Morse Potentials ◽  
Position Dependent Mass

Exact solutions of Schrödinger equation are obtained for the modified Kratzer and the corrected Morse potentials with the position-dependent effective mass. The bound state energy eigenvalues and the corresponding eigenfunctions are calculated for any angular momentum for target potentials. Various forms of point canonical transformations are applied.

Analytical solutions of fractional Schrödinger equation and thermal properties of Morse potential for some diatomic molecules

2021 ◽  
pp. 2150041
Author(s):  
U. S. Okorie ◽  
A. N. Ikot ◽  
G. J. Rampho ◽  
P. O. Amadi ◽  
Hewa Y. Abdullah
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Morse Potential ◽  
State Energy ◽  
Diatomic Molecules ◽  
Bound State ◽  
Bound State Energy ◽  
Fractional Schrödinger Equation ◽  
Energy Eigenvalues ◽  
Fractional Schrodinger Equation

By employing the concept of conformable fractional Nikiforov–Uvarov (NU) method, we solved the fractional Schrödinger equation with the Morse potential in one dimension. The analytical expressions of the bound state energy eigenvalues and eigenfunctions for the Morse potential were obtained. Numerical results for the energies of Morse potential for the selected diatomic molecules were computed for different fractional parameters chosen arbitrarily. Also, the graphical variation of the bound state energy eigenvalues of the Morse potential for hydrogen dimer with vibrational quantum number and the range of the potential were discussed, with regards to the selected fractional parameters. The vibrational partition function and other thermodynamic properties such as vibrational internal energy, vibrational free energy, vibrational entropy and vibrational specific heat capacity were evaluated in terms of temperature. Our results are new and have not been reported in any literature before.

scholarly journals Two-body bound state of ultracold Fermi atoms with two-dimensional spin-orbit coupling

2019 ◽  
Vol 100 (4) ◽  
Author(s):  
Shu Yang ◽  
Fan Wu ◽  
Wei Yi ◽  
Peng Zhang
Keyword(s):  
Bound State ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Two Dimensional

scholarly journals Relativistic study of the energy-dependent Coulomb potential including Coulomb-like tensor interaction

2012 ◽  
Vol 90 (7) ◽  
pp. 655-660 ◽  
Author(s):  
M. Hamzavi ◽  
S.M. Ikhdair
Keyword(s):  
Dirac Equation ◽  
Quantum Number ◽  
Coulomb Potential ◽  
Iteration Method ◽  
Arbitrary Spin ◽  
Tensor Interaction ◽  
Asymptotic Iteration Method ◽  
Spin Orbit ◽  
Energy Eigenvalues ◽  
Energy Dependent

The exact Dirac equation for the energy-dependent Coulomb (EDC) potential including a Coulomb-like tensor (CLT) potential has been studied in the presence of spin and pseudospin symmetries with arbitrary spin–orbit quantum number, κ. The energy eigenvalues and corresponding eigenfunctions are obtained in the framework of the asymptotic iteration method. Some numerical results are obtained in the presence and absence of EDC and CLT potentials.

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