Approximate Ro-Vibrational Spectrum of the Modified Rosen–Morse Molecular Potential Using the Nikiforov–Uvarov Method

2013 ◽  
Vol 68 (6-7) ◽  
pp. 427-432 ◽  
Author(s):  
Ali Akbar Rajabi ◽  
Majid Hamzavi
Keyword(s):  
Vibrational Spectrum ◽  
Schrodinger Equation ◽  
Approximation Scheme ◽  
Centrifugal Term ◽  
Energy Eigenvalues ◽  
Molecular Potential ◽  
Radial Schrödinger Equation ◽  
Uvarov Method ◽  
Nu Method ◽  
Good Agreement

By using the Nikiforov-Uvarov (NU) method and a new approximation scheme to the centrifugal term, we obtained the solutions of the radial Schrödinger equation (SE) for the modified Rosen- Morse (mRM) potential. In this paper, we get the approximate energy eigenvalues and show that the results are in good agreement with those obtained before. Eigenfunctions are also presented for completeness.

Solving of the Schrodinger equation analytically with an approximated scheme of the Woods–Saxon potential by the systematical method of Nikiforov–Uvarov

2020 ◽  
Vol 29 (06) ◽  
pp. 2050032
Author(s):  
Enayatolah Yazdankish
Keyword(s):  
Schrödinger Equation ◽  
Exponential Type ◽  
Schrodinger Equation ◽  
Analytic Solutions ◽  
Centrifugal Term ◽  
Saxon Potential ◽  
Energy Eigenvalues ◽  
Nu Method

The analytic solutions of the Schrodinger equation for the Woods–Saxon (WS) potential and also for the generalized WS potential are obtained for the [Formula: see text]-wave nonrelativistic spectrum, with an approximated form of the WS potential and centrifugal term. Due to this fact that the potential is an exponential type and the centrifugal is a radial term, we have to use an approximated scheme. First, the Nikiforov–Uvarov (NU) method is introduced in brief, which is a systematical method, and then Schrodinger equation is solved analytically. Energy eigenvalues and the corresponding eigenvector are derived analytically by using the NU method. After that, the generalized WS potential is discussed at the end.

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 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).

scholarly journals Study on the Applicability of Varshni Potential to Predict the Mass Spectra of the Quark-Antiquark Systems in a Non-relativistic Framework

2021 ◽  
Vol 14 (4) ◽  
pp. 339-347
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Mass Spectra ◽  
Laguerre Polynomials ◽  
Heavy Meson ◽  
Energy Eigenvalues ◽  
Relativistic Regime ◽  
Uvarov Method ◽  
Relativistic Framework ◽  
Good Agreement

Abstract: In this work, we obtain the Schrödinger equation solutions for the Varshni potential using the Nikiforov-Uvarov method. The energy eigenvalues are obtained in non-relativistic regime. The corresponding eigenfunction is obtained in terms of Laguerre polynomials. We applied the present results to calculate heavy-meson masses of charmonium cc ¯ and bottomonium bb ¯. The mass spectra for charmonium and bottomonium multiplets have been predicted numerically. The results are in good agreement with experimental data and the works of other researchers. Keywords: Schrödinger equation, Varshni potential, Nikiforov-Uvarov method, Heavy meson. PACs: 14.20.Lq; 03.65.-w; 14.40.Pq; 11.80.Fv.

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 Quarkonium masses in a hot QCD medium using conformable fractional of the Nikiforov–Uvarov method

2019 ◽  
Vol 34 (31) ◽  
pp. 1950201
Author(s):  
M. Abu-Shady
Keyword(s):  
Order Parameter ◽  
Dimensional Space ◽  
Binding Energies ◽  
Heavy Quarkonium ◽  
Energy Eigenvalues ◽  
Debye Mass ◽  
Higher Dimensional ◽  
Radial Schrödinger Equation ◽  
Uvarov Method ◽  
Nu Method

By using the conformable fractional of the Nikiforov–Uvarov (CF–NU) method, the radial Schrödinger equation is analytically solved. The energy eigenvalues and corresponding functions are obtained, in which the dependent temperature potential is employed. The effect of fraction-order parameter is studied on the heavy-quarkonium masses such as charmonium and bottomonium in a hot QCD medium in the 3D and the higher-dimensional space. This paper discusses the flavor dependence of their binding energies and explores the nature of dissociation by employing the perturbative, nonperturbative, and the lattice-parametrized form of the Debye masses in the medium-modified potential. A comparison is studied with recent works. We conclude that the fractional-order plays an important role in a hot QCD medium in the 3D with consideration of a form of the Debye mass.

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.

IMPROVED ARBITRARY l-STATE SOLUTIONS OF THE HULTHÉN POTENTIAL

2009 ◽  
Vol 24 (28n29) ◽  
pp. 5523-5529 ◽  
Author(s):  
WEN-CHAO QIANG ◽  
WEN LI CHEN ◽  
KAI LI ◽  
HUA-PING ZHANG
Keyword(s):  
Analytical Solutions ◽  
Approximate Formula ◽  
Approximation Scheme ◽  
Wave Functions ◽  
Centrifugal Term ◽  
Hulthén Potential ◽  
Energy Eigenvalues ◽  
Hulthen Potential ◽  
Radial Schrödinger Equation ◽  
Numerical Integration Methods

We developed a new and simple approximation scheme for centrifugal term. Using the new approximate formula for 1/r2 we derived approximately analytical solutions to the radial Schrödinger equation of the Hulthén potential with arbitrary l-states. Normalized analytical wave-functions are also obtained. Some energy eigenvalues are numerically calculated and compared with those obtained by C. S. Jia et al. and other methods such as the asymptotic iteration, the supersymmetry, the numerical integration methods and a Mathematica program, schroedinger, by W. Lucha and F. F. Schöberl.

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.

ARBITRARY l-WAVE BOUND STATE SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH THE ECKART POTENTIAL

2009 ◽  
Vol 23 (18) ◽  
pp. 2269-2279 ◽  
Author(s):  
YONG-FENG DIAO ◽  
LIANG-ZHONG YI ◽  
TAO CHEN ◽  
CHUN-SHENG JIA
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Approximation Scheme ◽  
Function Analysis ◽  
Bound State ◽  
Centrifugal Term ◽  
Radial Wave ◽  
Shape Invariance ◽  
Eckart Potential ◽  
Analytical Results

By using a modified approximation scheme to deal with the centrifugal term, we solve approximately the Schrödinger equation for the Eckart potential with the arbitrary angular momentum states. The bound state energy eigenvalues and the unnormalized radial wave functions are approximately obtained in a closed form by using the supersymmetric shape invariance approach and the function analysis method. The numerical experiments show that our analytical results are in better agreement with those obtained by using the numerical integration approach than the analytical results obtained by using the conventional approximation scheme to deal with the centrifugal term.

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