An asymptotic interation method for solving second-order homogeneous linear differential equations of the form y'' = lambda(x) y' + s(x) y is introduced, where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to Schroedinger type problems, including some with highly singular potentials, are presented.

https://arxiv.org/pdf/math-ph/0309066.pdf

Asymptotic iteration method for eigenvalue problems

We investigate the approximate solutions of the Dirac equation with the position-dependent mass particle in the Eckart potential field including the Coulomb tensor interaction by using the parametric Nikiforov-Uvarov method. Taking an appropriate approximation to deal with the centrifugal term, the Dirac energy states and the corresponding normalized two-spinor components of the wave function are obtained in closed form. Some special cases of our solution are investigated. Furthermore, we present the correct solutions obtained via the asymptotic iteration method which are in agreement with the parametric Nikiforov-Uvarov method results.

Bound states of spatially dependent mass Dirac equation with the Eckart potential including Coulomb tensor interaction

Numerical methods in laminar and turbulent flow

In this paper, we present the analytical solution of the radial Schrodinger equation for the Hulthen potential within the framework of the asymptotic iteration method by using an approximation to the centrifugal potential for any l states. We obtain the energy eigenvalues and corresponding eigenfunctions for different screening parameters. The wavefunctions are physical and energy eigenvalues are in good agreement with the results obtained by other methods for different δ values. In order to demonstrate this, the results of the asymptotic iteration method are compared with the results of the supersymmetry, numerical integration, variational and shifted 1/N expansion methods.

https://iopscience.iop.org/article/10.1088/0305-4470/39/37/012/pdf

Any l-state solutions of the Hulthen potential by the asymptotic iteration method

For any spin–orbit coupling term κ, the analytical solutions of the Dirac equation for the Eckart potential are presented by using the asymptotic iteration method within the framework of the spin and pseudospin symmetry concept. The energy eigenvalues are obtained in the closed form by applying an approximation to the spin–orbit coupling potential.

κ state solutions of the Dirac equation for the Eckart potential with pseudospin and spin symmetry

A simple exact analytical solution of the relativistic Duffin-Kemmer-Petiau equation within the framework of the asymptotic iteration method is presented. Exact bound state energy eigenvalues and corresponding eigenfunctions are determined for the relativistic harmonic oscillator as well as the Coulomb potentials. As a nontrivial example, the anharmonic oscillator is solved and the energy eigenvalues are obtained within the perturbation theory using the asymptotic iteration method.

Asymptotic iteration method solutions to the relativistic Duffin-Kemmer-Petiau equation

We present an alternative and simple method for the exact solution of the Klein-Gordon equation in the presence of the noncentral equal scalar and vector potentials by using Nikiforov-Uvarov method. The exact bound state energy eigenvalues and corresponding eigenfunctions are obtained for a particle bound in a potential of V(r,θ)=α∕r+β∕(r2sin2θ)+γcosθ∕(r2sin2θ) type.

Exact analytical solution to the relativistic Klein-Gordon equation with noncentral equal scalar and vector potentials

The general solutions of the Schrodinger equation for a non-central potential are obtained by using the Nikiforov–Uvarov method. The Schrodinger equation with general non-central potential is separated into radial and angular parts, and energy eigenvalues and eigenfunctions are derived analytically. By making special selections, the non-central potential is reduced to Coulomb and Hartmann ring-shaped potentials, and the obtained results are compared with the solutions of Coulomb and Hartmann potentials given in the literature.

https://iopscience.iop.org/article/10.1088/0305-4470/38/29/012/pdf

Exact solutions of the Schrödinger equation with non-central potential by the Nikiforov–Uvarov method

The general solutions of Schrodinger equation for non central potential are obtained by using Nikiforov Uvarov method. The Schrodinger equation with general non central potential is separated into radial and angular parts and energy eigenvalues and eigenfunctions for these potentials are derived analytically. Non central potential is reduced to Coulomb and Hartmann potential by making special selections, and the obtained solutions are compared with the solutions of Coulomb and Hartmann ring shaped potentials given in literature.

Exact solutions of the Schrodinger equation with non central potential by Nikiforov Uvarov method

We present an alternative and simple method for the exact solution of the Klein-Gordon equation in the presence of the non-central equal scalar and vector potentials by using Nikiforov-Uvarov (NU) method. The exact bound state energy eigenvalues and corresponding eigenfunctions are obtained for a particle bound in a potential of $V(r,\theta) = \frac{\alpha}{r} + \frac{\beta}{r^2\sin ^2\theta} + \gamma \frac{\cos \theta}{r^2\sin ^2\theta}$ type.

F. Yasuk

Papers

Asymptotic iteration method solutions to the relativistic Duffin-Kemmer-Petiau equation

Exact analytical solution to the relativistic Klein-Gordon equation with noncentral equal scalar and vector potentials

Exact solutions of the Schrödinger equation with non-central potential by the Nikiforov–Uvarov method

Exact solutions of the Schrodinger equation with non central potential by Nikiforov Uvarov method

Exact analytical solution to the relativistic Klein-Gordon equation with non-central equal scalar and vector potentials