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.

EXACT SOLUTIONS OF THE KLEIN–GORDON EQUATION FOR THE ROSEN–MORSE TYPE POTENTIALS VIA NIKIFOROV–UVAROV METHOD

2008 ◽  
Vol 23 (35) ◽  
pp. 3005-3013 ◽  
Author(s):  
A. REZAEI AKBARIEH ◽  
H. MOTAVALI
Keyword(s):  
Exact Solutions ◽  
Gordon Equation ◽  
Bound State ◽  
S Wave ◽  
Vector Potentials ◽  
Klein Gordon ◽  
The One ◽  
Uvarov Method ◽  
Equal Scalar ◽  
Klein Gordon Equation

The exact solutions of the one-dimensional Klein–Gordon equation for the Rosen–Morse type potential with equal scalar and vector potentials are presented. First, we briefly review Nikiforov–Uvarov mathematical method. Using this method, wave functions and corresponding exact energy equation are obtained for the s-wave bound state. It has been shown that the results for Rosen–Morse type potentials reduce to the standard Rosen–Morse well and Eckart potentials in the special case. The PT-symmetry for these potentials is also considered.

scholarly journals Surface interaction effects to a Klein–Gordon particle embedded in a Woods–Saxon potential well in terms of thermodynamic functions,

2018 ◽  
Vol 96 (7) ◽  
pp. 843-850 ◽  
Author(s):  
B.C. Lütfüoğlu
Keyword(s):  
Thermodynamic Functions ◽  
State Energy ◽  
Gordon Equation ◽  
Surface Effect ◽  
Bound State ◽  
Point Of View ◽  
Potential Well ◽  
Saxon Potential ◽  
Relativistic Regime ◽  
Klein Gordon

Recently, it has been investigated how the thermodynamic functions vary when the surface interactions are taken into account for a nucleon that is confined in a Woods–Saxon potential well, with a non-relativistic point of view. In this manuscript, the same problem is handled with a relativistic point of view. More precisely, the Klein–Gordon equation is solved in the presence of mixed scalar–vector generalized symmetric Woods–Saxon potential energy that is coupled to momentum and mass. Employing the continuity conditions the bound state energy spectra of an arbitrarily parameterized well are derived. It is observed that, when a term representing the surface effect is taken into account, the character of Helmholtz free energy and entropy versus temperature are modified in a similar fashion as this inclusion is done in the non-relativistic regime. Whereas it is found that this inclusion leads to different characters to internal energy and specific heat functions for relativistic and non-relativistic regimes.

scholarly journals APPROXIMATE ℓ-STATE SOLUTIONS TO THE KLEIN–GORDON EQUATION FOR MODIFIED WOODS–SAXON POTENTIAL WITH POSITION DEPENDENT MASS

2009 ◽  
Vol 24 (20n21) ◽  
pp. 3985-3994 ◽  
Author(s):  
ALTUĞ ARDA ◽  
RAMAZAN SEVER
Keyword(s):  
Approximation Scheme ◽  
Gordon Equation ◽  
Saxon Potential ◽  
Radial Part ◽  
Potential Term ◽  
Energy Eigenvalues ◽  
Klein Gordon ◽  
Uvarov Method ◽  
Dependent Mass ◽  
Klein Gordon Equation

The radial part of the Klein–Gordon equation for the generalized Woods–Saxon potential is solved by using the Nikiforov–Uvarov method with spatially dependent mass within the new approximation scheme to the centrifugal potential term. The energy eigenvalues and corresponding normalized eigenfunctions are computed. The solutions in the case of constant mass are also obtained to check out the consistency of our new approximation scheme.

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 Bound-State Solution of s-Wave Klein-Gordon Equation for Woods-Saxon Potential

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Eser Olğar ◽  
Haydar Mutaf
Keyword(s):  
Gordon Equation ◽  
Bound State ◽  
State Solution ◽  
Asymptotic Iteration Method ◽  
Saxon Potential ◽  
Bound State Solution ◽  
S Wave ◽  
Eigenvalues And Eigenfunctions ◽  
Klein Gordon ◽  
Klein Gordon Equation

The bound-state solution of s-wave Klein-Gordon equation is calculated for Woods-Saxon potential by using the asymptotic iteration method (AIM). The energy eigenvalues and eigenfunctions are obtained for the required condition of bound-state solutions.

Bound and scattering states solutions of the Klein–Gordon equation with the attractive radial potential in higher dimensions

2021 ◽  
Author(s):  
U. S. Okorie ◽  
A. N. Ikot ◽  
C. A. Onate ◽  
M. C. Onyeaju ◽  
G. J. Rampho
Keyword(s):  
Phase Shift ◽  
State Energy ◽  
Gordon Equation ◽  
Higher Dimensions ◽  
Bound State ◽  
Bound State Energy ◽  
Scattering States ◽  
Klein Gordon ◽  
Scattering Phase ◽  
Radial Potential

In this study, the Klein–Gordon equation (KGE) is solved with the attractive radial potential using the Nikiforov–Uvarov-functional-analysis (NUFA) method in higher dimensions. By employing the Greene–Aldrich approximation scheme, the approximate bound state energy equations as well as the corresponding radial wave function are obtained in closed form. Also, the expression for the scattering phase shift is obtained in D-dimensions. The effects of the screening parameter and the total angular momentum quantum number on the bound state energy and the scattering states’ phase shift are also studied numerically and graphically at different dimensions. An interesting result of this study is the inter-dimensional degeneracy symmetry for scattering phase shift. Hence, this concept is applicable in the areas of nuclear and particle physics.

scholarly journals BOUND STATES OF THE KLEIN–GORDON EQUATION FOR WOODS–SAXON POTENTIAL WITH POSITION DEPENDENT MASS

2008 ◽  
Vol 19 (05) ◽  
pp. 763-773 ◽  
Author(s):  
ALTUĞ ARDA ◽  
RAMAZAN SEVER
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
One Dimension ◽  
Saxon Potential ◽  
Energy Eigenvalues ◽  
Klein Gordon ◽  
Uvarov Method ◽  
Dependent Mass ◽  
Mass Case ◽  
Klein Gordon Equation

The effective mass Klein–Gordon equation in one dimension for the Woods–Saxon potential is solved by using the Nikiforov–Uvarov method. Energy eigenvalues and the corresponding eigenfunctions are computed. Results are also given for the constant mass case.

scholarly journals APPROXIMATE ℓ-STATE SOLUTIONS OF A SPIN-0 PARTICLE FOR WOODS–SAXON POTENTIAL

2009 ◽  
Vol 20 (04) ◽  
pp. 651-665 ◽  
Author(s):  
ALTUĞ ARDA ◽  
RAMAZAN SEVER
Keyword(s):  
Schrodinger Equation ◽  
Bound States ◽  
Gordon Equation ◽  
Saxon Potential ◽  
Radial Part ◽  
Centrifugal Barrier ◽  
Klein Gordon ◽  
Uvarov Method ◽  
Special Case ◽  
Klein Gordon Equation

The radial part of Klein–Gordon equation is solved for the Woods–Saxon potential within the framework of an approximation to the centrifugal barrier. The bound states and the corresponding normalized eigenfunctions of the Woods–Saxon potential are computed by using the Nikiforov–Uvarov method. The results are consistent with the ones obtained in the case of generalized Woods–Saxon potential. The solutions of the Schrödinger equation by using the same approximation are also studied as a special case, and obtained the consistent results with the ones obtained before.

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