Approximate Analytical Solutions of the Perturbed Yukawa Potential with Centrifugal Barrier

2013 ◽  
Vol 68 (6-7) ◽  
pp. 454-460 ◽  
Author(s):  
Ali Akbar Rajabi ◽  
Majid Hamzavi
Keyword(s):  
Analytical Solutions ◽  
Yukawa Potential ◽  
Energy Levels ◽  
Centrifugal Barrier ◽  
Energy Eigenvalues ◽  
Approximate Analytical Solutions ◽  
Screening Parameter ◽  
Radial Schrödinger Equation ◽  
Type Potential ◽  
Coulomb Potentials

By using the generalized parametric Nikiforov-Uvarov (NU) method, we have obtained the approximate analytical solutions of the radial Schrödinger equation for a perturbed Yukawa potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented and compared with the standard Yukawa potential. Further, we found the energy levels of the familiar Mie-type potential when the screening parameter of the perturbed Yukawa potential goes to zero, and finally, standard Yukawa and Coulomb potentials are discussed.

scholarly journals Energy States of Some Diatomaic Molecules: The Exact Quantisation Rule Approach

2015 ◽  
Vol 70 (2) ◽  
pp. 85-90 ◽  
Author(s):  
Babatunde J. Falaye ◽  
Sameer M. Ikhdair ◽  
Majid Hamzavi
Keyword(s):  
Hypergeometric Functions ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Molecular Potential ◽  
Approximate Analytical Solutions ◽  
Rule Approach ◽  
Radial Schrödinger Equation ◽  
Good Agreement

AbstractIn this study, we obtain the approximate analytical solutions of the radial Schrödinger equation for the Deng–Fan diatomic molecular potential by using the exact quantisation rule approach. The wave functions were expressed by hypergeometric functions via the functional analysis approach. An extension to the rotational–vibrational energy eigenvalues of some diatomic molecules is also presented. It is shown that the calculated energy levels are in good agreement with those obtained previously (Enℓ–D; shifted Deng–Fan).

Nonrelativistic treatment of hydrogen-like and neutral atoms subjected to the generalized perturbed Yukawa potential with centrifugal barrier in the symmetries of noncommutative quantum mechanics

2020 ◽  
Vol 17 (05) ◽  
pp. 2050067
Author(s):  
Abdelmadjid Maireche
Keyword(s):  
Potential Model ◽  
Yukawa Potential ◽  
Hamiltonian Operator ◽  
Real Space ◽  
Neutral Atoms ◽  
Centrifugal Barrier ◽  
Energy Eigenvalues ◽  
Quantum Numbers ◽  
Approximate Analytical Solutions ◽  
Generalized Gamma Function

We have obtained the approximate analytical solutions of the nonrelativistic Hydrogen-like atoms such as [Formula: see text] and [Formula: see text] and neutral atoms such as ([Formula: see text] and [Formula: see text]) atoms with a newly proposed generalized perturbed Yukawa potential with centrifugal barrier (GPYPCB) model using the generalized Bopp’s shift method and standard perturbation theory in the symmetries of noncommutative three-dimensional real space phase (NC: 3D-RSP). By approximating the centrifugal term through the Greene–Aldrich approximation scheme, we have obtained the energy eigenvalues and generalized Hamiltonian operator for all orbital quantum numbers [Formula: see text] in the symmetries of NC: 3D-RSP. The potential is a superposition of the perturbed Yukawa potential and new terms proportional with [Formula: see text]) appear as a result of the effects of noncommutativity properties of space and phase on the perturbed Yukawa potential model. The obtained energy eigenvalues appear as functions of the generalized Gamma function, the discreet atomic quantum numbers [Formula: see text], two infinitesimal parameters [Formula: see text], which are induced by (position–position and phase–phase). In addition, the dimensional parameters [Formula: see text] of perturbed Yukawa potential with centrifugal barrier model in NC: 3D-RSP. Furthermore, we have shown that the corresponding Hamiltonian operator in (NC: 3D-RSP) symmetries is the sum of the Hamiltonian operator of perturbed Yukawa potential model and the two operators are modified spin–orbit interaction and the modified Zeeman operator for the previous Hydrogenic and neutral atoms.

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).

APPROXIMATE RELATIVISTIC κ-STATE SOLUTIONS TO THE DIRAC-HYPERBOLIC PROBLEM WITH GENERALIZED TENSOR INTERACTIONS

2013 ◽  
Vol 22 (07) ◽  
pp. 1350048 ◽  
Author(s):  
AKPAN N. IKOT ◽  
H. HASSANABADI ◽  
B. H. YAZARLOO ◽  
S. ZARRINKAMAR
Keyword(s):  
Dirac Equation ◽  
Analytical Solutions ◽  
Tensor Interaction ◽  
Numerical Results ◽  
Hyperbolic Problem ◽  
Energy Eigenvalues ◽  
Approximate Analytical Solutions ◽  
Frame Work ◽  
Nu Method

In this paper, we present the approximate analytical solutions of the Dirac equation for hyperbolical potential within the frame work of spin and pseudospin symmetries limit including the newly proposed generalized tensor interaction (GTI) using the Nikiforov–Uvarov (NU) technique. We obtained the energy eigenvalues and the corresponding eigenfunction using the generalized parametric NU method. The numerical results of our work reveal that the presence of the GTI changes the degeneracy between the spin and pseudospin state doublets.

scholarly journals A PERTURBATIVE TREATMENT FOR THE ENERGY LEVELS OF NEUTRAL ATOMS

2006 ◽  
Vol 21 (31) ◽  
pp. 6465-6476 ◽  
Author(s):  
SAMEER M. IKHDAIR ◽  
RAMAZAN SEVER
Keyword(s):  
Entire Range ◽  
Potential Model ◽  
Yukawa Potential ◽  
Energy Levels ◽  
Binding Energies ◽  
Neutral Atoms ◽  
Large N ◽  
Perturbative Method ◽  
Screening Parameter ◽  
Perturbative Treatment

Energy levels of neutral atoms have been reexamined by applying an alternative perturbative scheme in solving the Schrödinger equation for the Yukawa potential model with a modified screening parameter. The predicted shell binding energies are found to be quite accurate over the entire range of the atomic number Z up to 84 and compare very well with those obtained within the framework of hypervirial-Padé scheme and the method of shifted large-N expansion. It is observed that the new perturbative method may also be applied to the other areas of atomic physics.

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.

DKP EQUATION UNDER A VECTOR HULTHÉN-TYPE POTENTIAL: AN APPROXIMATE SOLUTION

2011 ◽  
Vol 26 (22) ◽  
pp. 1621-1629 ◽  
Author(s):  
S. ZARRINKAMAR ◽  
A. A. RAJABI ◽  
H. RAHIMOV ◽  
H. HASSANABADI
Keyword(s):  
Quantum Mechanics ◽  
Approximate Solution ◽  
Analytical Solutions ◽  
Hulthén Potential ◽  
Dkp Equation ◽  
Hulthen Potential ◽  
Approximate Analytical Solutions ◽  
Supersymmetry Quantum Mechanics ◽  
Type Potential

Approximate analytical solutions of Duffin–Kemmer–Petiau equation are obtained for a vector Hulthén potential. The solutions are reported for any J-state using an elegant approximation and methodology of supersymmetry quantum mechanics.

Eigensolutions and theoretic quantities under the nonrelativistic wave equation

2020 ◽  
Vol 19 (02) ◽  
pp. 2050007
Author(s):  
C. A. Onate ◽  
L. S. Adebiyi ◽  
D. T. Bankole
Keyword(s):  
Wave Function ◽  
Energy Equation ◽  
Radial Wave Function ◽  
Tsallis Entropy ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Screening Parameter ◽  
Radial Schrödinger Equation ◽  
Information Energy ◽  
Uvarov Method

The radial Schrödinger equation was solved with the combination of three important potentials with [Formula: see text] as deformed parameter via the parametric Nikiforov–Uvarov method and the energy equation as well as the corresponding normalized radial wave function were obtained in close and compact form. The energy equation obtained was used to study eight molecules. The effect of the deformed parameter on energy eigenvalues was also studied numerically. The subset of the combined potential was also studied numerically and the results were found to be in agreement with the previous results. To extend the application of our work, the wave function obtained was used to calculate some theoretic quantities such as the Tsallis entropy, Rényi entropy and information energy. By putting the Tsallis index to 2, we deduced the information energy from Tsallis entropy. Finally, the effect of the deformed parameter and screening parameter, respectively, on the theoretic quantities were also studied.

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