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

The Tietz-Hua (TH) potential is one of the very best analytical model potentials for the vibrational energy of diatomic molecules. By using the Nikiforov-Uvarov method, we have obtained the exact analytical s-wave solutions of the radial Schrodinger equation for the TH potential. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. Some numerical results for diatomic molecules are also presented. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

The rotation‐vibration spectrum of diatomic molecules with the tietz‐hua rotating oscillator

Supersymmetric solution of the Schroedinger equation for Woods-Saxon potential by using the Pekeris approximation

There is now motivating experimental evidence for relativistic symmetries in nuclei and hadrons, namely pseudospin and spin symmetry limits of the Dirac equation besides the old theoretical backgrounds. The most fundamental ingredients in such studies are definitely the wave functions and energy eigenvalues. Here, having in mind the importance of the Coulomb term as well as the degeneracy-removing role of tensor interaction, we obtain the exact solutions to the problem for Coulomb scalar, vector and tensor terms in both spin and pseudospin symmetry limits. We see that, contrary to many other common cumbersome techniques, the problem is simply solved via the methodology of supersymmetric quantum mechanics.

Dirac Equation for a Coulomb Scalar, Vector and Tensor Interaction

We solve the Dirac equation with the Eckart potential including a Coulomb-like tensor potential under pseudospin symmetry limit with arbitrary spin-orbit coupling quantum number κ by using the Nikiforov-Uvarov method. We have obtained closed forms of eigenfunctions, energy eigenvalues and compared our results with other present data.

Ali Akbar Rajabi

Papers

The rotation‐vibration spectrum of diatomic molecules with the tietz‐hua rotating oscillator

Supersymmetric solution of the Schroedinger equation for Woods-Saxon potential by using the Pekeris approximation

Dirac Equation for a Coulomb Scalar, Vector and Tensor Interaction

Approximate Pseudospin Solutions of the Dirac Equation with the Eckart Potential Including a Coulomb-Like Tensor Potential

Dirac equation in the presence of coulomb and linear terms in (1 + 1) dimensions; the supersymmetric approach