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 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.

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 Diatomic Molecules and Mass Spectrum of Heavy Quarkonium System with Kratzer- Screened Coulomb Potential (KSCP) through the Solutions of the Schrödinger Equation

2021 ◽  
Vol 3 (2) ◽  
pp. 48-55
Author(s):  
E. P. Inyang ◽  
E. P. Inyang ◽  
J. Karniliyus ◽  
J. E. Ntibi ◽  
E. S. William
Keyword(s):  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Diatomic Molecules ◽  
Expansion Method ◽  
Bound State ◽  
Heavy Quarkonium ◽  
Energy Eigenvalues ◽  
Special Cases ◽  
Screened Coulomb Potential

In this work, we obtain solutions of the Schrödinger equation with Kratzer-screened Coulomb potential (KSCP) model using the series expansion method. Explicitly, we compute the bound state energy eigenvalues for selected diatomic molecules of N2, CO, NO, and CH, respectively, for the various vibrational and rotational quantum states and the numerical energy eigenvalues agree with the existing literature. Three special cases were considered. The energy eigenvalues are applied to obtain the mass spectra of heavy quarkonium system such as charmonium and bottomonium. The results agree with the experimental data and other recent theoretical studies.

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 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.

ANALYTICAL APPROXIMATIONS TO THE SCHRÖDINGER EQUATION FOR A SECOND PÖSCHL–TELLER-LIKE POTENTIAL WITH CENTRIFUGAL TERM

2008 ◽  
Vol 23 (10) ◽  
pp. 1537-1544 ◽  
Author(s):  
SHI-HAI DONG ◽  
WEN-CHAO QIANG ◽  
J. GARCÍA-RAVELO
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound State ◽  
Centrifugal Term ◽  
Short Range Potential ◽  
Quantum Numbers ◽  
Analytical Approximations ◽  
Special Cases ◽  
Arbitrary Quantum ◽  
Good Agreement

The bound state solutions of the Schrödinger equation for a second Pöschl–Teller-like potential with the centrifugal term are obtained approximately. It is found that the solutions can be expressed in terms of the hypergeometric functions 2F1(a, b; c; z). To show the accuracy of our results, we calculate the eigenvalues numerically for arbitrary quantum numbers n and l. It is found that the results are in good agreement with those obtained by other method for short-range potential. Two special cases for l = 0 and V1 = V2 are also studied briefly.

scholarly journals Arbitrary l-Solutions of the Schrodinger Equation in Arbitrary Dimensions for the Energy Dependent Generalized Inverse Quadratic Yukawa Potential

2021 ◽  
Vol 3 (2) ◽  
pp. 34-43
Author(s):  
P. O. Ushie ◽  
C. M. Ekpo ◽  
T. O. Magu ◽  
P. O. Okoi
Keyword(s):  
Schrödinger Equation ◽  
Potential Energy ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Generalized Inverse ◽  
Yukawa Potential ◽  
Bound State ◽  
Energy Eigenvalues ◽  
Special Cases ◽  
Energy Dependent

Within the framework of Nikiforov-Uvarov method, we obtained an approximate solution of the Schrodinger equation for the Energy Dependent Generalized inverse quadratic Yukawa potential model. The bound state energy eigenvalues for were computed for various vibrational and rotational quantum numbers. Special cases were considered when the potential parameters were altered, resulting into Energy Dependent Kratzer and Kratzer potential, Energy Dependent Kratzer fues and Kratzer fues potential, Energy Dependent Inverse quadratic Yukawa and Inverse quadratic Yukawa Potential, Energy Dependent Yukawa (screened Coulomb) and Yukawa (screened Coulomb) potential, and Energy Dependent Coulomb and Coulomb potential, respectively. Their energy eigenvalues expressions and numerical computations agreed with the already existing literatures.

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.

ANALYTICAL APPROXIMATIONS TO THE l-WAVE SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH A HYPERBOLIC POTENTIAL

2008 ◽  
Vol 22 (07) ◽  
pp. 483-489 ◽  
Author(s):  
SHISHAN DONG ◽  
S. G. MIRANDA ◽  
F. M. ENRIQUEZ ◽  
SHI-HAI DONG
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Bound State ◽  
Short Range Potential ◽  
Quantum Numbers ◽  
Analytical Approximations ◽  
Special Cases ◽  
Hyperbolic Potential ◽  
Arbitrary Quantum

The bound-state solutions of the Schrödinger equation for a hyperbolic potential with the centrifugal term are presented approximately. It is shown that the solutions can be expressed by the hypergeometric function 2F1(a, b; c; z). To show the accuracy of our results, we calculate the energy levels numerically for arbitrary quantum numbers n and l. It is found that the results are in good agreement with those obtained by other methods for short-range potential. Two special cases for l = 0 and σ = 1 are also studied briefly.

scholarly journals Arbitrary l-solutions of the Schrödinger equation interacting with Hulthén – Hellmann potential model

2020 ◽  
Vol 66 (6 Nov-Dec) ◽  
pp. 730 ◽  
Author(s):  
E. S. William ◽  
E. P. Inyang ◽  
E. A. Thompson
Keyword(s):  
Schrödinger Equation ◽  
Quantum State ◽  
Schrodinger Equation ◽  
Potential Model ◽  
Bound State ◽  
Energy Eigenvalues ◽  
Special Cases ◽  
Radial Schrödinger Equation ◽  
Hellmann Potential ◽  
Good Agreement

In this study, we obtained bound state solutions of the radial Schrödinger equation by the superposition of Hulthén plus Hellmann potential within the framework of Nikiforov-Uvarov (NU) method for an arbitrary  - states. The corresponding normalized wave functions expressed in terms of Jacobi polynomial for a particle exposed to this potential field was also obtained. The numerical energy eigenvalues for different quantum state have been computed. Six special cases are also considered and their energy eigenvalues are obtained. Our results are found to be in good agreement with the results in literature. The behavior of energy in the ground and excited state for different quantum state are studied graphically.

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