scholarly journals An improved approximation scheme for the centrifugal term and the Hulthén potential

2009 ◽  
Vol 39 (3) ◽  
pp. 307-314 ◽  
Author(s):  
S. M. Ikhdair
Keyword(s):  
Approximation Scheme ◽  
Centrifugal Term ◽  
Hulthén Potential ◽  
Hulthen 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

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.

The scattering states of the generalized Hulthén potential with an improved new approximate scheme for the centrifugal term

2009 ◽  
Vol 18 (9) ◽  
pp. 3663-3669 ◽  
Author(s):  
Wei Gao-Feng ◽  
Chen Wen-Li ◽  
Wang Hong-Ying ◽  
Li Yuan-Yuan
Keyword(s):  
Centrifugal Term ◽  
Hulthén Potential ◽  
Hulthen Potential ◽  
Scattering States ◽  
Approximate Scheme

scholarly journals Approximate analytical solutions for arbitrary l-state of the Hulthén potential with an improved approximation of the centrifugal term

2011 ◽  
Vol 9 (4) ◽  
pp. 737-742 ◽  
Author(s):  
Jerzy Stanek
Keyword(s):  
Bound State ◽  
Centrifugal Term ◽  
Approximate Methods ◽  
Quantization Rule ◽  
Hulthén Potential ◽  
Hulthen Potential ◽  
Approximate Analytical Solutions ◽  
Exact Quantization Rule ◽  
Screening Parameter ◽  
Uvarov Method

AbstractAn approximate analytical solution of the radial Schrödinger equation for the generalized Hulthén potential is obtained by applying an improved approximation of the centrifugal term. The bound state energy eigenvalues and the normalized eigenfunctions are given in terms of hypergeometric polynomials. The results for arbitrary quantum numbers n r and l with different values of the screening parameter δ are compared with those obtained by the numerical method, asymptotic iteration, the Nikiforov-Uvarov method, the exact quantization rule, and variational methods. The results obtained by the method proposed in this work are in a good agreement with those obtained by other approximate methods.

ARBITRARY l-WAVE SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH THE HULTHÉN POTENTIAL MODEL

2009 ◽  
Vol 24 (24) ◽  
pp. 4519-4528 ◽  
Author(s):  
CHUN-SHENG JIA ◽  
YONG-FENG DIAO ◽  
LIANG-ZHONG YI ◽  
TAO CHEN
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Function Analysis ◽  
Bound State ◽  
Centrifugal Term ◽  
Hulthén Potential ◽  
Radial Wave ◽  
Hulthen Potential ◽  
Analytical Results ◽  
Screening Parameter

By using an improved new approximation scheme to deal with the centrifugal term, we investigate the bound state solutions of the Schrödinger equation with the Hulthén potential for the arbitrary angular momentum number. The bound state energy spectra and the unnormalized radial wave functions have been approximately obtained by using the supersymmetric shape invariance approach and the function analysis method. The numerical experiments show that our approximate analytical results are in better agreement with those obtained by using numerical integration approach for small values of the screening parameter δ than the other analytical results obtained by using the conventional approximation to the centrifugal term.

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.

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.

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