scholarly journals Pekeris approximation – another perspective

2013 ◽  
Vol 377 (42) ◽  
pp. 3027-3032 ◽  
Author(s):  
F.J.S. Ferreira ◽  
F.V. Prudente
Keyword(s):  
Pekeris Approximation

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 Spin and Pseudospin Symmetry in Generalized Manning-Rosen Potential

2015 ◽  
Vol 2015 ◽  
pp. 1-17 ◽  
Author(s):  
Hilmi Yanar ◽  
Ali Havare
Keyword(s):  
Dirac Equation ◽  
Bound States ◽  
Pseudospin Symmetry ◽  
Molecular Structures ◽  
Centrifugal Term ◽  
Term Energy ◽  
Energy Relations ◽  
Rosen Potential ◽  
Uvarov Method ◽  
Pekeris Approximation

Spin and pseudospin symmetric Dirac spinors and energy relations are obtained by solving the Dirac equation with centrifugal term for a new suggested generalized Manning-Rosen potential which includes the potentials describing the nuclear and molecular structures. To solve the Dirac equation the Nikiforov-Uvarov method is used and also applied the Pekeris approximation to the centrifugal term. Energy eigenvalues for bound states are found numerically in the case of spin and pseudospin symmetry. Besides, the data attained in the present study are compared with the results obtained in the previous studies and it is seen that our data are consistent with the earlier ones.

scholarly journals The bound state solutions of the D-dimensional Schrödinger equation for the Woods–Saxon potential

2016 ◽  
Vol 25 (01) ◽  
pp. 1650002 ◽  
Author(s):  
V. H. Badalov
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound State ◽  
Wave Functions ◽  
Saxon Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Quantum Numbers ◽  
Radial Schrödinger Equation ◽  
Pekeris Approximation

In this work, the analytical solutions of the [Formula: see text]-dimensional radial Schrödinger equation are studied in great detail for the Wood–Saxon potential by taking advantage of the Pekeris approximation. Within a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any angular momentum case within the context of the Nikiforov–Uvarov (NU) and Supersymmetric quantum mechanics (SUSYQM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformed each other is demonstrated. In addition, a finite number energy spectrum depending on the depth of the potential [Formula: see text], the radial [Formula: see text] and orbital [Formula: see text] quantum numbers and parameters [Formula: see text] are defined as well.

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.

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 ANY l-STATE SOLUTIONS OF THE WOODS–SAXON POTENTIAL IN ARBITRARY DIMENSIONS WITHIN THE NEW IMPROVED QUANTIZATION RULE

2010 ◽  
Vol 25 (20) ◽  
pp. 3941-3952 ◽  
Author(s):  
SAMEER M. IKHDAIR ◽  
RAMAZAN SEVER
Keyword(s):  
Effective Potential ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Centrifugal Term ◽  
Saxon Potential ◽  
S Wave ◽  
Quantization Rule ◽  
Energy Eigenvalues ◽  
Arbitrary Dimensions ◽  
Pekeris Approximation

The approximated energy eigenvalues and the corresponding eigenfunctions of the spherical Woods–Saxon effective potential in D dimensions are obtained within the new improved quantization rule for all l-states. The Pekeris approximation is used to deal with the centrifugal term in the effective Woods–Saxon potential. The interdimensional degeneracies for various orbital quantum number l and dimensional space D are studied. The solutions for the Hulthén potential, the three-dimensional (D = 3), the s-wave (l = 0) and the cases are briefly discussed.

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