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

Ta-Pei Cheng and Ling-Fong Li 1984 Clarendon Press: Oxford University Press xi + 536 pp price £35 (£15 paperback) ISBN 0 19 851956 7 Hdbk, 0 19 851961 3Pbk This book is an excellent summary of gauge theories in particle physics, intended for advanced graduate students and research workers in the field. It presupposes both a knowledge of elementary particle phenomenology and of quantum field theory at the level taught in first-year postgraduate lecture courses.

https://iopscience.iop.org/article/10.1088/0031-9112/36/5/028/pdf

Gauge Theory of Elementary Particle Physics

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

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

An evaluation of A = 16{17 was published in Nuclear Physics A565 (1993), p. 1. This version of A = 16 diers from the published version in that we have corrected some errors discovered after the article went to press. It has also been slightly revised as of May 16 ,200 0t oinclud ehyperlink sfo rreference san dtables. Introductor ytables have been omitted from this manuscript. Also, Reference key numbers have been changed to the NNDC/TUNL format.

Energy Levels of Light Nuclei A =1 6

Dirac equation for the harmonic scalar and vector potentials and linear plus coulomb-like tensor potential; the SUSY approach

Exact pseudospin symmetry solution of the Dirac equation for spatially-dependent mass Coulomb potential including a Coulomb-like tensor interaction via asymptotic iteration method

We study the D-dimensional Schrodinger equation for an energy-dependent Hamiltonian that linearly depends on energy and quadratically on the relative distance. Next, via the Nikiforov—Uvarov (NU) method, we calculate the corresponding eigenfunctions and eigenvalues.

https://iopscience.iop.org/article/10.1088/0253-6102/55/4/01/pdf

Exact Solutions of D-Dimensional Schrödinger Equation for an Energy-Dependent Potential by NU Method

The Yukawa potential is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov-Uvarov method, we obtain approximate analytical solutions of the radial Schrodinger equation for the Yukawa potential. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented and show that these results are in good agreement with those obtained previously by other methods. Also, we find the energy levels of the familiar pure Coulomb potential energy levels when the screening parameter of the Yukawa potential goes to zero.

https://iopscience.iop.org/article/10.1088/0256-307X/29/8/080302/pdf

Approximate Analytical Solution of the Yukawa Potential with Arbitrary Angular Momenta

Approximate analytical solutions of a Duffin-Kemmer-Petiau (DKP) equation are obtained via an elegant ansatz after successive transformations. Apart from the wide application of the DKP equation in both cosmology and theoretical nuclear physics as well as the physical significance of the Coulomb interaction, this is particularly important as we have provided a solution to the corresponding Heun equation.

Ali Akbar Rajabi

Papers

Dirac equation for the harmonic scalar and vector potentials and linear plus coulomb-like tensor potential; the SUSY approach

Exact pseudospin symmetry solution of the Dirac equation for spatially-dependent mass Coulomb potential including a Coulomb-like tensor interaction via asymptotic iteration method

Exact Solutions of D-Dimensional Schrödinger Equation for an Energy-Dependent Potential by NU Method

Approximate Analytical Solution of the Yukawa Potential with Arbitrary Angular Momenta

Duffin-Kemmer-Petiau equation under a scalar Coulomb interaction