scholarly journals Exact Bound State Solutions of the Schrödinger Equation for Noncentral Potential via the Nikiforov-Uvarov Method

2009 ◽  
Vol 48 (7) ◽  
pp. 2154-2163 ◽  
Author(s):  
Metin Aktaş
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound State ◽  
Exact Bound ◽  
Noncentral Potential ◽  
Uvarov Method

scholarly journals Bound State Solutions of the Hua Potential within the Framework of Two Approximations Scheme

2021 ◽  
Vol 3 (3) ◽  
pp. 38-41
Author(s):  
E. B. Ettah ◽  
P. O. Ushie ◽  
C. M. Ekpo
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Equation ◽  
Bound State ◽  
S Wave ◽  
Angular Momenta ◽  
Special Cases ◽  
Uvarov Method

In this paper, we solve analytically the Schrodinger equation for s-wave and arbitrary angular momenta with the Hua potential is investigated respectively. The wave function as well as energy equation are obtained in an exact analytical manner via the Nikiforov Uvarov method using two approximations scheme. Some special cases of this potentials are also studied.

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 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 solutions of the Schrödinger equation with energy-dependent molecular Kratzer potential via asymptotic iteration method

2020 ◽  
Vol 45 (1) ◽  
pp. 65 ◽  
Author(s):  
Akpan Ndem Ikot ◽  
Uduakobong Okorie ◽  
Alalibo Thompson Ngiagian ◽  
Clement Atachegbe Onate ◽  
Collins Okon Edet ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Iteration Method ◽  
Schrodinger Equation ◽  
Graphical Representation ◽  
Bound State ◽  
Confluent Hypergeometric Function ◽  
Asymptotic Iteration Method ◽  
Slope Parameter ◽  
Exact Bound ◽  
Energy Dependent

In this paper, we obtained the exact bound state energy spectrum of the Schrödinger equation with energy dependent molecular Kratzer potential using asymptotic iteration method (AIM). The corresponding wave function expressed in terms of the confluent hypergeometric function was also obtained. As a special case, when the energy slope parameter in the energy-dependent molecular Kratzer potential is set to zero, then the well-known molecular Kratzer potential is recovered. Numerical results for the energy eigenvlaues are also obtained for different quantum states, in the presence and absence of the energy slope parameter. These results are discussed extensively using graphical representation. Our results are seen to agree with the results in literature.

scholarly journals Analytical Solution of the Schrödinger Equation with Spatially Varying Effective Mass for Generalised Hylleraas Potential

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Sanjib Meyur ◽  
Smarajit Maji ◽  
S. Debnath
Keyword(s):  
Schrödinger Equation ◽  
Effective Mass ◽  
Schrodinger Equation ◽  
Hypergeometric Functions ◽  
State Energy ◽  
Bound State ◽  
Exact Bound ◽  
Effective Mass Schrödinger Equation ◽  
Spatially Varying ◽  
Special Case

We have obtained exact solution of the effective mass Schrödinger equation for the generalised Hylleraas potential. The exact bound state energy eigenvalues and corresponding eigenfunctions are presented. The bound state eigenfunctions are obtained in terms of the hypergeometric functions. Results are also given for the special case of potential parameter.

scholarly journals STATISTICAL ANALYSIS AND INFORMATION THEORY OF SCREENED KRATZER-HELLMANN POTENTIAL MODEL

2021 ◽  
Author(s):  
G.T. Osobonye ◽  
U.S. Okorie ◽  
P.O. Amadi ◽  
A.N. Ikot
Keyword(s):  
Schrödinger Equation ◽  
Fisher Information ◽  
Shannon Entropy ◽  
Schrodinger Equation ◽  
Potential Model ◽  
Bound State ◽  
Screening Parameter ◽  
Hellmann Potential ◽  
Information Theoretic Measures ◽  
Uvarov Method

In this research, the radial Schrodinger equation for a newly proposed screened Kratzer-Hellmann potential model was studied via the conventional Nikiforov-Uvarov method. The approximate bound state solution of the Schrodinger equation was obtained using the Greene-Aldrich approximation in addition to the normalized eigenfunction for the new potential model, both analytically and numerically. These results were employed to evaluate the rotational-vibrational partition function and other thermodynamic properties for the screened Kratzer-Hellmann potential. The results obtained have been graphically discussed. Also, the normalized eigenfunction has been used to calculate some information-theoretic measures including Shannon entropy and Fisher information for low lying states in both position and momentum spaces numerically. The Shannon entropy results obtained agreed with the Bialynicki-Birula and Mycielski inequality, while the Fisher information results obtained agreed with the Stam, Crammer-Rao inequality. Also, an alternating increasing and decreasing localization across the screening parameter for both eigenstates were observed.

EXACT SOLUTIONS OF THE SCHRÖDINGER EQUATION FOR A NEW RING-SHAPED NONHARMONIC OSCILLATOR POTENTIAL

2008 ◽  
Vol 23 (12) ◽  
pp. 1919-1927 ◽  
Author(s):  
YAN-FU CHENG ◽  
TONG-QING DAI
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Laguerre Polynomials ◽  
Bound State ◽  
Wave Functions ◽  
Oscillator Potential ◽  
Radial Wave ◽  
Generalized Laguerre Polynomials ◽  
Uvarov Method ◽  
Special Case

The bound state solutions of the Schrödinger equation with a new ring-shaped nonharmonic potential are presented using exactly the Nikiforov–Uvarov method. It is found that the solutions of the angular wave function can be expressed by Jacobi polynomial and radial wave functions are given by the generalized Laguerre polynomials. We also discuss the special case for α = 0 and β = 0 respectively.

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