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

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

On the Klein–Gordon oscillator subject to a Coulomb-type potential

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

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.

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

The authors investigate solutions of the three dimensional Klein-Gordon and Schrodinger equations in the presence of a new exactly solvable potential of V(r,θ)=−2De(re∕r−(1∕2)(re2∕r2))+b∕r2sin2θ+a∕r2cos2θ type, the so-called double ring-shaped Kratzer potential. For a diatomic molecule system in double ring-shaped Kratzer potential, the exact bound state energy eigenvalues and corresponding wave functions have been determined within the framework of the asymptotic iteration method. Bound state eigenfunction solutions used in applications related to molecular spectroscopy are obtained in terms of confluent hypergeometric function and Jacobi polynomial. This new formulation is tested by calculating the energies of rovibrational states of a number of diatomic molecules. Also, the author-prove that in the nonrelativistic limit c→∞, where c is the speed of light, solutions of the Klein-Gordon system converge to those of the Schrodinger system.

Relativistic and nonrelativistic solutions for diatomic molecules in the presence of double ring-shaped Kratzer potential

The three dimensional Klein–Gordon equation is solved with a double ring-shaped oscillator for the case of the equal vector and scalar potential, , by using the asymptotic iteration method which is very efficient, systematic and practical. The bound states energy eigenvalues and corresponding eigenfunctions are presented for a particle bound in a potential of a double ring-shaped oscillator.

Aysen Durmus

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

Relativistic and nonrelativistic solutions for diatomic molecules in the presence of double ring-shaped Kratzer potential

Relativistic solutions for double ring-shaped oscillator potential via asymptotic iteration method