English
Related papers

Related papers: An Improvement of the Asymptotic Iteration Method …

200 papers

The Schrodinger equation for the rotational-vibrational (ro-vibrational) motion of a diatomic molecule with empirical potential functions is solved approximately by means of the Nikiforov-Uvarov method. The approximate ro-vibratinal energy…

Quantum Physics · Physics 2009-10-09 Sameer M. Ikhdair , Ramazan Sever

We consider a single particle which is bound by a central potential and obeys the Dirac equation in d dimensions. We first apply the asymptotic iteration method to recover the known exact solutions for the pure Coulomb case. For a…

Mathematical Physics · Physics 2009-11-11 Hakan Ciftci , Richard L. Hall , Nasser Saad

The Nikiforov-Uvarov method is a simple, yet elegant and powerful method for solving second-order differential equations of generalized hypergeometric type. In the past, it has been used to solve many problems in quantum mechanics and…

Quantum Physics · Physics 2025-05-13 Abdaljalel E. Alizzi , Alina E. Sagaydak , Zurab K. Silagadze

In this paper, we derive an asymptotic error expansion for the eigenvalue approximations by the lowest order Raviart-Thomas mixed finite element method for the general second order elliptic eigenvalue problems. Extrapolation based on such…

Numerical Analysis · Mathematics 2011-01-11 Hehu Xie

The asymptotic iteration method is used to find exact and approximate solutions of Schroedinger's equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent).…

Mathematical Physics · Physics 2014-03-05 Hakan Ciftci , Richard L. Hall , Nasser Saad

In this study, we obtain the approximate analytical solutions of the radial Schrodinger equation for the New Generalized Morse-Like Potential in arbitrary dimensions by using the Nikiforov Uvarov Method. Energy eigenvalues and corresponding…

Quantum Physics · Physics 2020-12-07 C. M. Ekpo , Ephraim P. Inyang , P. O. Okoi , T. O. Magu , E. P. Agbo , K O Okorie , Etido P. Inyang

We review the so-called Nikiforov-Uvarov method along with some basic results about classical orthogonal polynomials and hypergeometric functions related to the hypergeometric differential equation. The method is employed to address certain…

Classical Analysis and ODEs · Mathematics 2024-11-05 Guillermo Gordillo-Núñez

We discuss the existence of solutions with oblique asymptotes to a class of second order nonlinear ordinary differential equations by means of Lyapunov functions. The approach is new in this field and allows for simpler proofs of general…

Classical Analysis and ODEs · Mathematics 2010-01-06 Octavian G. Mustafa , Cemil Tunc

There are some types of ill-conditioned algebraic equations that have difficulty in obtaining accurate roots and coefficients that must be expressed with a multiple precision floating-point number. When all their roots are simple, the…

Numerical Analysis · Mathematics 2023-02-07 Tomonori Kouya

This is a response to a recently reported comment [1] on paper [J. Math. Phys.59, 082105 (2018)] regarding the quantization of damped harmonic oscillator using a non-Hermitian Hamiltonian with real energy eigenvalues. We assert here that…

Quantum Physics · Physics 2019-09-26 M. Serhan , M. Abusini , Ahmed Al-Jamel , H. El-Nasser , Eqab M. Rabei

In this paper it is shown how to solve numerically eigenvalue problems associated to second order linear ordinary differential equations, containing also terms which depend on the variable. A didactic presentation of the Numerov Method is…

Quantum Physics · Physics 2021-10-19 F. Caruso , V. Oguri

Exact solution of the Dirac equation for a special form of the Woods-Saxon potential is obtained for the s-states. The energy eigenvalues and two-component spinor wave functions are derived by using a systematical method which is called as…

Nuclear Theory · Physics 2009-11-11 Cuneyt Berkdemir , Ayse Berkdemir , Ramazan Sever

The Schr\"{o}dinger equation is solved exactly for some well known potentials. Solutions are obtained reducing the Schr\"{o}dinger equation into a second order differential equation by using an appropriate coordinate transformation. The…

Quantum Physics · Physics 2019-12-06 Cevdet Tezcan , Ramazan Sever

Asymptotic iteration method (AIM) is used to find the exact analytical solutions of the one dimensional Klein-Gordon equation for the q-deformed Manning-Rosen potential with equal Lorentz vector and scalar potential. The bound state…

Quantum Physics · Physics 2017-02-24 Tapas Das

This paper is concerned with the design and analysis of a fully adaptive eigenvalue solver for linear symmetric operators. After transforming the original problem into an equivalent one formulated on $\ell_2$, the space of square summable…

Numerical Analysis · Mathematics 2007-11-08 W. Dahmen , T. Rohwedder , R. Schneider , A. Zeiser

The solvability of The Dirac equation is studied for the exponential-type potentials with the pseudospin symmetry by using the parametric generalization of the Nikiforov-Uvarov method. The energy eigenvalue equation, and the corresponding…

Quantum Physics · Physics 2015-05-14 Altug Arda , Ramazan Sever , Cevdet Tezcan

Using the Nikiforov-Uvarov method, the bound state energy eigenvalues and eigenfunctions of the PT-/non-PT-symmetric and non-Hermitian generalized Woods-Saxon (WS) potential with the real and complex-valued energy levels are obtained in…

Quantum Physics · Physics 2009-04-21 Sameer M. Ikhdair , Ramazan Sever

For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit…

Numerical Analysis · Mathematics 2026-01-12 Shengyue Wang , Aihui Zhou

In this article we consider the discretely self-similar singular solutions of the Euler equations, and the possible velocity profiles concerned not only have decaying spatial asymptotics, but also have unconventional non-decaying…

Analysis of PDEs · Mathematics 2015-03-03 Liutang Xue

We propose an iterative finite element method for solving non-linear hydromagnetic and steady Euler's equations. Some three-dimensional computational tests are given to confirm the convergence and the high efficiency of the method.

Numerical Analysis · Mathematics 2009-12-01 Cédric Boulbe , Tahar Zamène Boulmezaoud , T. Amari