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 APPROXIMATE ℓ-STATE SOLUTION OF TIME INDEPENDENT SCHRÖDINGER WAVE EQUATION WITH MODIFIED MÖBIUS SQUARED POTENTIAL PLUS HULTHÉN POTENTIAL

2020 ◽  
Vol 4 (2) ◽  
pp. 425-435
Author(s):  
Dlama Yabwa ◽  
Eyube E.S ◽  
Yusuf Ibrahim
Keyword(s):  
State Energy ◽  
Approximation Scheme ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Hulthén Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Type Approximation ◽  
Hulthen Potential

In this work we have applied ansatz method to solve for the approximate ℓ-state solution of time independent Schrödinger wave equation with modified Möbius squared potential plus Hulthén potential to obtain closed form expressions for the energy eigenvalues and normalized radial wave-functions. In dealing with the spin-orbit coupling potential of the effective potential energy function, we have employed the Pekeris type approximation scheme, using our expressions for the bound state energy eigenvalues, we have deduced closed form expressions for the bound states energy eigenvalues and normalized radial wave-functions for Hulthén potential, modified Möbius square potential and Deng-Fan potential. Using the value 0.976865485225 for the parameter ω, we have computed bound state energy eigenvalues for various quantum states (in atomic units). We have also computed bound state energy eigenvalues for six diatomic molecules: HCl, LiH, TiH, NiC, TiC and ScF. The results we obtained are in near perfect agreement with numerical results in the literature and a clear demonstration of the superiority of the Pekeris-type approximation scheme over the Greene and Aldrich approximation scheme for the modified Möbius squares potential plus Hulthén potential.

A new approximation scheme for the centrifugal term and the Hulthén potential

2008 ◽  
Vol 372 (27-28) ◽  
pp. 4779-4782 ◽  
Author(s):  
Chun-Sheng Jia ◽  
Jian-Yi Liu ◽  
Ping-Quan Wang
Keyword(s):  
Approximation Scheme ◽  
Centrifugal Term ◽  
Hulthén Potential ◽  
Hulthen Potential

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.

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.

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.

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.

Arbitrary /-state approximate solutions of the Hulthén potential through the exact quantization rule

Open Physics ◽  
2008 ◽  
Vol 6 (2) ◽  
Author(s):  
Wen-Chao Qiang ◽  
Yang Gao ◽  
Run-Suo Zhou
Keyword(s):  
Bound States ◽  
Energy Levels ◽  
Approximate Solutions ◽  
Quantization Rule ◽  
Hulthén Potential ◽  
Hulthen Potential ◽  
Approximate Analytical Solutions ◽  
Exact Quantization Rule ◽  
Radial Schrödinger Equation ◽  
Numerical Integration Methods

AbstractIn this paper, using the Exact Quantization Rule, we present approximate analytical solutions of the radial Schrödinger equation with non-zero l values for the Hulthén potential in the frame of an approximation to the centrifugal potential for any l states. The energy levels of all bound states can be easily calculated from the Exact Quantization Rule. Specifically, the normalized analytical wave functions are also obtained. Some energy eigenvalues are numerically calculated and compared with those obtained by other methods such as asymptotic iteration, supersymmetry, numerical integration methods, and the schroedinger Mathematica package.

PSEUDOSPIN AND SPIN SYMMETRY FOR THE RING-SHAPED GENERALIZED HULTHÉN POTENTIAL

2010 ◽  
Vol 25 (21) ◽  
pp. 4067-4079 ◽  
Author(s):  
OKTAY AYDOĞDU ◽  
RAMAZAN SEVER
Keyword(s):  
State Energy ◽  
Spin Symmetry ◽  
Bound State ◽  
Wave Functions ◽  
Relativistic Energy ◽  
Hulthén Potential ◽  
Energy Eigenvalues ◽  
Hulthen Potential ◽  
Dependent Part ◽  
Uvarov Method

We obtain the bound state energy eigenvalues and the corresponding wave functions of the Dirac particle for the generalized Hulthén potential plus a ring-shaped potential with pseudospin and spin symmetry. The Nikiforov–Uvarov method is used in the calculations. Contribution of the angle-dependent part of the potential to the relativistic energy spectra are investigated. In addition, it is shown that the obtained results coincide with those available in the literature.

scholarly journals The Nonrelativistic Scattering States of the Deng-Fan Potential

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Bentol Hoda Yazarloo ◽  
Liangliang Lu ◽  
Guanghui Liu ◽  
Saber Zarrinkamar ◽  
Hassan Hassanabadi
Keyword(s):  
Approximation Scheme ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Scattering States ◽  
Special Cases ◽  
Scattering State ◽  
Term Energy ◽  
Scattering Phase ◽  
Scattering Phase Shifts ◽  
Nonrelativistic Scattering

The approximately analytical scattering state solution of the Schrodinger equation is obtained for the Deng-Fan potential by using an approximation scheme to the centrifugal term. Energy eigenvalues, normalized wave functions, and scattering phase shifts are calculated. We consider and verify two special cases: thel=0and thes-wave Hulthén potential.

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