The General Solution for Bound States of the Woods–Saxon Potential

2020 ◽  
pp. 109-118
Keyword(s):  
General Solution ◽  
Bound States ◽  
Saxon Potential

scholarly journals Dirac Particle for the Position Dependent Mass in the Generalized Asymmetric Woods-Saxon Potential

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Soner Alpdoğan ◽  
Ali Havare
Keyword(s):  
Bound States ◽  
Dirac Particle ◽  
Saxon Potential ◽  
One Dimensional ◽  
Transmission And Reflection Coefficients ◽  
Scattering States ◽  
Transmission Resonances ◽  
The One ◽  
Dependent Mass ◽  
Position Dependent Mass

The one-dimensional Dirac equation with position dependent mass in the generalized asymmetric Woods-Saxon potential is solved in terms of the hypergeometric functions. The transmission and reflection coefficients are obtained by considering the one-dimensional electric current density for the Dirac particle and the equation describing the bound states is found by utilizing the continuity conditions of the obtained wave function. Also, by using the generalized asymmetric Woods-Saxon potential solutions, the scattering states are found out without making calculation for the Woods-Saxon, Hulthen, cusp potentials, and so forth, which are derived from the generalized asymmetric Woods-Saxon potential and the conditions describing transmission resonances and supercriticality are achieved. At the same time, the data obtained in this work are compared with the results achieved in earlier studies and are observed to be consistent.

scholarly journals Scattering, bound, and quasi-bound states of the generalized symmetric Woods-Saxon potential

2016 ◽  
Vol 57 (3) ◽  
pp. 032103 ◽  
Author(s):  
B. C. Lütfüoğlu ◽  
F. Akdeniz ◽  
O. Bayrak
Keyword(s):  
Bound States ◽  
Saxon Potential

SUPERSYMMETRY APPROACHES TO THE BOUND STATES OF THE GENERALIZED WOODS–SAXON POTENTIAL

2004 ◽  
Vol 19 (08) ◽  
pp. 615-625 ◽  
Author(s):  
H. FAKHRI ◽  
J. SADEGHI
Keyword(s):  
Differential Equation ◽  
Quantum Mechanics ◽  
Bound States ◽  
Differential Operators ◽  
Energy Levels ◽  
Negative Energy ◽  
Saxon Potential ◽  
First Order ◽  
Jacobi Differential Equation ◽  
Algebraic Solutions

Using the associated Jacobi differential equation, we obtain exactly bound states of the generalization of Woods–Saxon potential with the negative energy levels based on the analytic approach. According to the supersymmetry approaches in quantum mechanics, we show that these bound states by four pairs of the first-order differential operators, represent four types of the laddering equations. Two types of these supersymmetry structures, suggest the derivation of algebraic solutions by two different approaches for the bound states.

scholarly journals Remarks on the Woods–Saxon potential

2016 ◽  
Vol 31 (23) ◽  
pp. 1650134 ◽  
Author(s):  
M. Çapak ◽  
B. Gönül
Keyword(s):  
Angular Momentum ◽  
Closed Form ◽  
Nuclear Structure ◽  
Analytical Solutions ◽  
Bound States ◽  
Collective Model ◽  
Saxon Potential ◽  
Related Literature ◽  
Exact Solvability ◽  
Approximate Analytical Solutions

More recently, comprehensive applications of approximate analytical solutions of the Woods–Saxon (WS) potential in closed form for the five-dimensional Bohr Hamiltonian have appeared [M. Çapak, D. Petrellis, B. Gönül and D. Bonatsos, J. Phys. G 42, 95102 (2015)] and its comparison to the data for many different nuclei has clearly revealed the domains for the success and failure in case of using such potential forms to analyze the data related to the nuclear structure within the frame of the collective model. Gaining confidence from this work, the exact solvability of the WS type potentials in lower dimensions for the bound states having zero angular momentum is carefully reviewed to finalize an ongoing discussion in the related literature which clearly shows that such kind of potentials have no analytical solutions even for [Formula: see text] case.

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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