Related papers: An Improvement of the Asymptotic Iteration Method …
Analytical solutions are presented for eigenvalues, eigenfunctions of {\color{red} D-dimensional Schrodinger equation having Eckart potential} within Nikiforov-Uvarov method. This uses a new, improved approximation for centrifugal term,…
We study asymptotics of eigenvalues, eigenfunctions and norming constants of singular energy-dependent Sturm--Liouville equations with complex-valued potentials. The analysis essentially exploits the integral representation of solutions,…
In this work we discuss the possibility to reduce the computational complexity of modal methods, i.e. methods based on eigenmodes expansion, from the third power to the second power of the number of eigenmodes. The proposed approach is…
We consider solutions of the $2\times 2$ matrix Hamiltonian of physical systems within the context of the asymptotic iteration method. Our technique is based on transformation of the associated Hamiltonian in the form of the first order…
In this article, we present the analytical solution of the radial Schr\"{o}dinger equation for the Hulth\'{e}n potential within the framework of the asymptotic iteration method by using an approximation to the centrifugal potential for any…
We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…
We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focussing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the…
This paper is part of a series of papers in which the asymptotic theory and appropriate symbolic computer code are developed to compute the asymptotic expansion of the solution of an n-th order ordinary differential equation. The paper…
This paper addresses the problem of finding an asymptotic solution for first and second order integro-differential equations containing an arbitrary kernel, by evaluating the corresponding inverse Laplace and Fourier transforms. The aim of…
The Nikiforov-Uvarov method is employed to calculate the the Schrodinger equation with a rotation Morse potential. The bound state energy eigenvalues and the corresponding eigenfunction are obtained. All of these calculation present an…
In the iterative algorithm recently proposed by Waxman for solving eigenvalue problems, we point out that the convergence rate may be improved. For many non-singular symmetric potentials which vanish asymptotically, a simple analytical…
In a previous paper (J. Phys. A 36, 11807 (2003)), we introduced the `asymptotic iteration method' for solving second-order homogeneous linear differential equations. In this paper, we study perturbed problems in quantum mechanics and we…
We give a study of some molecular vibration potentials by solving the D-dimensional Schrodinger equation using the asymptotic iteration method (AIM). The eigenvalue values obtained by the AIM are found to agree with analytic solutions. The…
We develop symbolic methods of asymptotic approximations for solutions of linear ordinary differential equations and use to them stabilize numerical calculations. Our method follows classical analysis for first-order systems and…
The one-dimensional spinless Salpeter equation has been solved for the PT-symmetric generalized Hulth\'{e}n potential. The Nikiforov-Uvarov {NU) method which is based on solving the second-order linear differential equations by reduction to…
We provide an elementary proof of the asymptotic behavior of solutions of second order differential equations.
Analytical solutions of the N-dimensional Schr\"odinger equation for the newly proposed Varshni-Hulth\'en potential are obtained within the framework of Nikiforov-Uvarov method by using Greene-Aldrich approximation scheme to the centrifugal…
We study the long time behaviour of the solutions of the third grade fluids equations in dimension 2. Introducing scaled variables and performing several energy estimates in weighted Sobolev spaces, we describe the first order of an…
For applications to quasi-exactly solvable Schr\"odinger equations in quantum mechanics, we establish the general conditions that have to be satisfied by the coefficients of a second-order differential equation with at most $k+1$ singular…
The creation and annihilation operators of a two-term diatomic molecular potential are studied and it is observed that they satisfy the commutation relations of a SU(1,1) algebra. To study the Lie algebraic realization of the present…