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.

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.

APPROXIMATE BOUND DIRAC STATES FOR PSEUDOSCALAR HULTHÉN POTENTIAL

2013 ◽  
Vol 22 (06) ◽  
pp. 1350035
Author(s):  
M. HAMZAVI ◽  
A. A. RAJABI ◽  
F. KOOCHAKPOOR
Keyword(s):  
Dirac Equation ◽  
Energy Eigenvalue ◽  
Spin Symmetry ◽  
Bound State ◽  
Hulthén Potential ◽  
Energy Eigenvalues ◽  
Hulthen Potential ◽  
Approximate Analytical Solutions ◽  
Potential Parameters ◽  
Nu Method

In this paper, we present approximate analytical solutions of the Dirac equation with the pseudoscalar Hulthén potential under spin and pseudospin (p-spin) symmetry limits in (3+1) dimensions. The energy eigenvalues and corresponding eigenfunctions are given in their closed forms by using the Nikiforov–Uvarov (NU) method. Numerical results of the energy eigenvalue equations are presented to show the effects of the potential parameters on the bound-state energies.

scholarly journals Effect of the deformation parameter on the nonrelativistic energy spectra of the q-deformed Hulthen-quadratic exponential-type potential

2021 ◽  
Vol 46 (4) ◽  
pp. 60-73
Author(s):  
Ushie Patrick Obogo ◽  
Ofem Egbe Ubi ◽  
Collins Okon Edet ◽  
Akpan Ndem Ikot
Keyword(s):  
Exponential Type ◽  
Bound State ◽  
Energy Spectra ◽  
Hulthén Potential ◽  
Hulthen Potential ◽  
Special Cases ◽  
Atomic And Molecular Physics ◽  
Uvarov Method ◽  
Potential Parameters ◽  
Type Potential

In this study, an approximate solution of the Schr�dinger equation for the q-deformed Hulthen-quadratic exponential-type potential model within the framework of the Nikiforov�Uvarov method was obtained. The bound state energy equation and the corresponding eigenfunction was obtained. The energy spectrum is applied to study H2, HCl, CO and LiH diatomic molecules. The effect of the deformation parameters and other potential parameters on the energy spectra of the system were graphically and numerically analyzed in detail. Special cases were considered when the potential parameters were altered, resulting in deformed Hulthen potential, Hulthen potential, deformed quadratic exponential-type potential and quadratic exponential-type potential. The energy eigenvalues expressions agreed with what obtained in literature. Finally, the results can find many applications in quantum chemistry, atomic and molecular physics.

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.

scholarly journals Relativistic Symmetries of Hulthén Potential Incorporated with Generalized Tensor Interactions

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
A. N. Ikot ◽  
H. Hassanabadi ◽  
E. Maghsoodi ◽  
S. Zarrinkamar
Keyword(s):  
State Energy ◽  
Bound State ◽  
Tensor Interaction ◽  
Wave Functions ◽  
Energy Spectra ◽  
Bound State Energy ◽  
Hulthén Potential ◽  
Radial Wave ◽  
Hulthen Potential ◽  
Uvarov Method

Spin and pseudospin symmetries of the Dirac equation for a Hulthén potential with a novel tensor interaction, that is, a combination of the Coulomb and Yukawa potentials, are investigated using the Nikiforov-Uvarov method. The bound-state energy spectra and the radial wave functions are approximately obtained in the case of spin and pseudospin symmetries. The tensor interactions and the degeneracy-removing role are presented in details.

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.

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 Study on energy and information-entropic measures of Hulthén potential in D dimension by an intuitive approximation to centrifugal term

2021 ◽  
Author(s):  
D Nath ◽  
Amlan Roy
Keyword(s):  
Arbitrary Dimension ◽  
Centrifugal Term ◽  
Complexity Measures ◽  
Hulthén Potential ◽  
Approximate Analytical Expression ◽  
Hulthen Potential ◽  
Analytic Expressions ◽  
Heisenberg Uncertainty ◽  
Uvarov Method ◽  
Pekeris Approximation

Energy spectrum as well as various information theoretic measures are considered for Hulthén potential in D dimension. For a given ℓ≠0 state, analytic expressions are derived, following a simple intuitive approximation for accurate representation of centrifugal term, within the conventional Nikiforov-Uvarov method. This is derived from a linear combination of two widely used Greene-Aldrich and Pekeris-type approximations. Energy, wave function, normalization constant, expectation value in r and p space, Heisenberg uncertainty relation, entropic moment of order α¯, Shannon entropy, Rényi entropy, disequilibrium, majorization as well as four selected complexity measures like LMC (López-Ruiz, Mancini, Calbert), shape Rényi complexity, Generalized Rényi complexity and Rényi complexity ratio are offered for different screening parameters (δ). The effective potential is described quite satisfactorily throughout the whole domain. Obtained results are compared with theoretical energies available in literature, which shows excellent agreement. Performance of six different approximations to centrifugal term is critically discussed. An approximate analytical expression for critical screening for a specific state in arbitrary dimension is offered. Additionally, some inter-dimensional degeneracy occurring in two states, at different dimension for a particular δ is also uncovered. PACS: 02.60.-x, 03.65.Ca, 03.65.Ge, 03.65.-w Keywords: Hulthén potential, Rényi complexity ratio, Statistical complexity, Majorization, Pekeris approximation, Greene-Aldrich approximation.

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