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 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.

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.

ACCURATE ITERATIVE AND PERTURBATIVE SOLUTIONS OF THE YUKAWA POTENTIAL

2006 ◽  
Vol 15 (06) ◽  
pp. 1253-1262 ◽  
Author(s):  
M. KARAKOC ◽  
I. BOZTOSUN
Keyword(s):  
Numerical Methods ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
State Energy ◽  
Yukawa Potential ◽  
Bound State ◽  
Asymptotic Iteration Method ◽  
Bound State Energy ◽  
Energy Eigenvalues ◽  
Radial Schrödinger Equation

We apply the asymptotic iteration method to solve the radial Schrödinger equation for the Yukawa type potentials. The solution of the radial Schrödinger equation by using different approaches requires tedious and cumbersome calculations; however, we present that it is possible to obtain the bound state energy eigenvalues for any n and ℓ values easily within the framework of this method. We also show the perturbed application of this method for the same potential. Our results are in excellent agreement with the findings of the SUSY perturbation, 1/N expansion and numerical methods.

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.

SOLUTIONS OF THE SCHRODINGER EQUATION WITH INVERSELY QUADRATIC YUKAWA PLUS WOODS-SAXON POTENTIAL USING NIKIFOROV-UVAROV METHOD

2015 ◽  
Vol 8 (2) ◽  
pp. 2094-2098
Author(s):  
Benedict Ita ◽  
A. I. Ikeuba ◽  
O. Obinna
Keyword(s):  
State Energy ◽  
Jacobi Polynomials ◽  
Bound State ◽  
Negative Energy ◽  
Saxon Potential ◽  
Energy Eigenvalues ◽  
Eigen Values ◽  
Uvarov Method ◽  
Special Case ◽  
Nu Method

The solutions of the SchrÓ§dinger equation with inversely quadratic Yukawa plus Woods-Saxon potential (IQYWSP) have been presented using the parametric Nikiforov-Uvarov (NU) method. The bound state energy eigenvalues and the corresponding un-normalized eigen functions are obtained in terms of Jacobi polynomials. Also, a special case of the potential has been considered and its energy eigen values obtained. The result of the work could be applied to molecules moving under the influence of IQYWSP potential as negative energy eigenvalues obtained indicate a bound state system.

scholarly journals Solutions of the Schrödinger equation for pseudo-Coulomb potential plus a new improved ring-shaped potential in the cosmic string space–time

2016 ◽  
Vol 94 (5) ◽  
pp. 517-521 ◽  
Author(s):  
Akpan N. Ikot ◽  
Tamunoimi M. Abbey ◽  
Ephraim O. Chukwuocha ◽  
Michael C. Onyeaju
Keyword(s):  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Cosmic String ◽  
Schrodinger Equation ◽  
State Energy ◽  
Bound State ◽  
Space Time ◽  
Minkowski Space Time ◽  
Uvarov Method ◽  
Good Agreement

In this paper, we obtain the bound state energy eigenvalues and the corresponding eigenfunctions of the Schrödinger equation for the pseudo-Coulomb potential plus a new improved ring-shaped potential within the framework of cosmic string space–time using the generalized parametric Nikiforov–Uvarov method. Our results are in good agreement with other works in the cosmic string space–time and reduced to those in the Minkowski space–time when α = 1.

scholarly journals Solutions of Schrodinger equation and thermal properties of generalized trigonometric Poschl-Teller potential.

2020 ◽  
Vol 66 (6 Nov-Dec) ◽  
pp. 824
Author(s):  
C. O. Edet ◽  
P. O. Amadi ◽  
U. S. Okorie ◽  
A. Tas ◽  
A. N. Ikot ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Hypergeometric Functions ◽  
Energy Equation ◽  
Bound State ◽  
Energy Spectra ◽  
Energy Eigenvalues ◽  
Quantum Numbers ◽  
Special Cases ◽  
Potential Parameters

Analytical solutions of the Schrödinger equation for the generalized trigonometric Pöschl–Teller potential by using an appropriate approximation to the centrifugal term within the framework of the Functional Analysis Approach have been considered. Using the energy equation obtained, the partition function was calculated and other relevant thermodynamic properties. More so, we use the concept of the superstatistics to also evaluate the thermodynamics properties of the system. It is noted that the well-known normal statistics results are recovered in the absence of the deformation parameter and this is displayed graphically for the clarity of our results. We also obtain analytic forms for the energy eigenvalues and the bound state eigenfunction solutions are obtained in terms of the hypergeometric functions. The numerical energy spectra for different values of the principal and orbital quantum numbers are obtained. To show the accuracy of our results, we discuss some special cases by adjusting some potential parameters and also compute the numerical eigenvalue of the trigonometric Pöschl–Teller potential for comparison sake. However, it was found out that our results agree excellently with the results obtained via other methods

scholarly journals Closed Analytical Solutions of the D-Dimensional Schrödinger Equation with Deformed Woods–Saxon Potential Plus Double Ring-Shaped Potential

2016 ◽  
Vol 71 (1) ◽  
pp. 59-68 ◽  
Author(s):  
Mohamed Chabab ◽  
Abdelwahed El Batoul ◽  
Mustapha Oulne
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Hypergeometric Functions ◽  
Asymptotic Iteration Method ◽  
Saxon Potential ◽  
Double Ring ◽  
Ring Shape ◽  
Rule Approach ◽  
Uvarov Method ◽  
Pekeris Approximation

AbstractBy employing the Pekeris approximation, the D-dimensional Schrödinger equation is solved for the nuclear deformed Woods–Saxon potential plus double ring-shaped potential within the framework of the asymptotic iteration method (AIM). The energy eigenvalues are given in a closed form, and the corresponding normalised eigenfunctions are obtained in terms of hypergeometric functions. Our general results reproduce many predictions obtained in the literature, using the Nikiforov–Uvarov method (NU) and the improved quantisation rule approach, particularly those derived by considering Woods–Saxon potential without deformation and/or without ring shape interaction.

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