scholarly journals Eigensolutions of the N-dimensional Schrödinger equation interacting with Varshni-Hulthén potential model

2021 ◽  
Vol 67 (2 Mar-Apr) ◽  
pp. 193
Author(s):  
E. P. Inyang ◽  
E. S. William ◽  
J. A. Obu
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Approximation Scheme ◽  
Jacobi Polynomials ◽  
Hulthén Potential ◽  
Centrifugal Barrier ◽  
Energy Eigenvalues ◽  
Hulthen Potential ◽  
Special Cases ◽  
Uvarov Method

Analytical solutions of the N-dimensional Schrödinger equation for the newly proposed Varshni-Hulthén potential are obtained within the framework of Nikiforov-Uvarov method by using Greene-Aldrich approximation scheme to the centrifugal barrier. The numerical energy eigenvalues and the corresponding normalized eigenfunctions are obtained in terms of Jacobi polynomials. Special cases of the potential are equally studied and their numerical energy eigenvalues are in agreement with those obtained previously with other methods. However, the behavior of the energy for the ground state and several excited states is illustrated graphically.

scholarly journals Solusi Persamaan Schrödinger untuk Potensial Hulthen + Non-Sentral Poschl-Teller dengan Menggunakan Metode Nikiforov-Uvarov

2016 ◽  
Vol 3 (02) ◽  
pp. 169
Author(s):  
Nani Sunarmi ◽  
Suparmi S ◽  
Cari C
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Jacobi Polynomials ◽  
Energy Levels ◽  
Hulthén Potential ◽  
Central Potential ◽  
Hulthen Potential ◽  
Hypergeometric Type ◽  
Angular Equation ◽  
Uvarov Method

<span>The Schrödinger equation for Hulthen potential plus Poschl-Teller Non-Central potential is <span>solved analytically using Nikiforov-Uvarov method. The radial equation and angular equation <span>are obtained through the variable separation. The solving of Schrödinger equation with <span>Nikivorov-Uvarov method (NU) has been done by reducing the two order differensial equation <span>to be the two order differential equation Hypergeometric type through substitution of <span>appropriate variables. The energy levels obtained is a closed function while the wave functions <span>(radial and angular part) are expressed in the form of Jacobi polynomials. The Poschl-Teller <span>Non-Central potential causes the orbital quantum number increased and the energy of the <span>Hulthen potential is increasing positively.</span></span></span></span></span></span></span></span><br /></span>

Analytical bound-state solutions of the Schrödinger equation for the Manning–Rosen plus Hulthén potential within SUSY quantum mechanics

2018 ◽  
Vol 33 (03) ◽  
pp. 1850021 ◽  
Author(s):  
A. I. Ahmadov ◽  
Maria Naeem ◽  
M. V. Qocayeva ◽  
V. A. Tarverdiyeva
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Jacobi Polynomials ◽  
Bound State ◽  
Wave Functions ◽  
Hulthén Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Hulthen Potential

In this paper, the bound-state solution of the modified radial Schrödinger equation is obtained for the Manning–Rosen plus Hulthén potential by using new developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial wave functions are defined for any [Formula: see text] angular momentum case via the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. Thanks to both methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is presented. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary [Formula: see text] states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to [Formula: see text] radial and [Formula: see text] orbital quantum numbers.

scholarly journals Any l-State Solutions of the Schrodinger Equation for q-Deformed Hulthen Plus Generalized Inverse Quadratic Yukawa Potential in Arbitrary Dimensions

2019 ◽  
Vol 65 (4 Jul-Aug) ◽  
pp. 333 ◽  
Author(s):  
C. O. Edet ◽  
And P. O. Okoi
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Jacobi Polynomials ◽  
Generalized Inverse ◽  
Yukawa Potential ◽  
Bound State ◽  
Energy Eigenvalues ◽  
Special Cases ◽  
Different Dimensions ◽  
Arbitrary Dimensions

The bound state approximate solution of the Schrodinger equation is obtained for the q-deformed Hulthen plus generalized inverse quadratic Yukawa potential (HPGIQYP) in -dimensions using the Nikiforov-Uvarov (NU) method and the corresponding eigenfunctions are expressed in Jacobi polynomials. Seven special cases of the potential are discussed and the numerical energy eigenvalues are calculated for two values of the deformation parameter in different dimensions.

The bound state solutions of the D-dimensional Schrödinger equation for the Hulthén potential within SUSY quantum mechanics

2017 ◽  
Vol 26 (05) ◽  
pp. 1750028 ◽  
Author(s):  
H. I. Ahmadov ◽  
M. V. Qocayeva ◽  
N. Sh. Huseynova
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Dimensional Space ◽  
Energy Levels ◽  
Wave Functions ◽  
Hulthén Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Hulthen Potential

In this paper, the analytical solutions of the [Formula: see text]-dimensional hyper-radial Schrödinger equation are studied in great detail for the Hulthén potential. Within the framework, a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any [Formula: see text] orbital angular momentum case within the context of the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transforming each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary [Formula: see text] states for [Formula: see text]-dimensional space.

Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential

Open Physics ◽  
2008 ◽  
Vol 6 (3) ◽  
Author(s):  
Sameer Ikhdair ◽  
Ramazan Sever
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound States ◽  
Jacobi Polynomials ◽  
Wave Functions ◽  
Three Dimensions ◽  
Eigenvalues And Eigenfunctions ◽  
Energy Eigenvalues ◽  
Pseudoharmonic Potential ◽  
Uvarov Method

AbstractA new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring-shaped potential, is solved. It has the form $$ V(r,\theta ) = \tfrac{1} {8}\kappa r_e^2 \left( {\tfrac{r} {{r_e }} - \tfrac{{r_e }} {r}} \right)^2 + \tfrac{{\beta cos^2 \theta }} {{r^2 sin^2 \theta }} $$. The energy eigenvalues and eigenfunctions of the bound-states for the Schrödinger equation in D-dimensions for this potential are obtained analytically by using the Nikiforov-Uvarov method. The radial and angular parts of the wave functions are obtained in terms of orthogonal Laguerre and Jacobi polynomials. We also find that the energy of the particle and the wave functions reduce to the energy and the wave functions of the bound-states in three dimensions.

REAL SPECTRUM OF NON-HERMITIAN HAMILTONIANS FOR HULTHÉN POTENTIAL

2008 ◽  
Vol 23 (25) ◽  
pp. 2077-2084 ◽  
Author(s):  
SANJIB MEYUR ◽  
S. DEBNATH
Keyword(s):  
State Energy ◽  
Jacobi Polynomials ◽  
Bound State ◽  
Real Spectrum ◽  
Eigenvalues And Eigenfunctions ◽  
Hulthén Potential ◽  
Exact Bound ◽  
Energy Eigenvalues ◽  
Hulthen Potential ◽  
Uvarov Method

The non-Hermitian Hamiltonians of the type [Formula: see text] is solved for the generalized Hulthén potential in terms of Jacobi polynomials by using Nikiforov–Uvarov method. The exact bound-state energy eigenvalues and eigenfunctions are presented.

scholarly journals Analytical solutions of the Schrödinger equation for the Hulthén potential within SUSY quantum mechanics

2015 ◽  
Vol 30 (32) ◽  
pp. 1550193 ◽  
Author(s):  
H. I. Ahmadov ◽  
Sh. I. Jafarzade ◽  
M. V. Qocayeva
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Hulthén Potential ◽  
Shape Invariance ◽  
Hulthen Potential ◽  
Radial Schrödinger Equation ◽  
Uvarov Method ◽  
Ordinary Quantum

The analytical solution of the modified radial Schrödinger equation for the Hulthén potential is obtained within ordinary quantum mechanics by applying the Nikiforov–Uvarov method and supersymmetric quantum mechanics by applying the shape invariance concept that was introduced by Gendenshtein method by using the improved approximation scheme to the centrifugal potential for arbitrary l states. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary l states.

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.

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