Extension of Nikiforov-Uvarov Method for the Solution of Heun Equation

We report an alternative method to solve second order differential equations which have at most four singular points. This method is developed by changing the degrees of the polynomials in the basic equation of Nikiforov-Uvarov (NU) method. This is called extended NU method for this paper. The eigenvalue solutions of Heun equation and confluent Heun equation are obtained via extended NU method. Some quantum mechanical problems such as Coulomb problem on a 3-sphere, two Coulombically repelling electrons on a sphere and hyperbolic double-well potential are investigated by this method

Solution of Schrödinger equation for two different potentials using extended Nikiforov-Uvarov method and polynomial solutions of biconfluent Heun equation

Exact solutions of the Schrödinger equation for two different potentials are presented by using the extended Nikiforov-Uvarov method. The first one is the inverse square root potential which is a long-range potential and the second one is a combination of Coulomb, linear, and harmonic potentials which is often used to describe quarkonium. Eigenstate solutions are obtained in a systematic way without using any ansatz or transformation. Eigenfunctions for considered potentials are given in terms of biconfluent Heun polynomials. © 2018 Author(s).This work has been supported by Kirklareli University under the Research Project No. KLUBAP142. -

Analytical exact solutions for the Razavy type potential

Atman, Kazim Gokhan/0000-0001-8800-9736WOS: 000541374700001A quantum system with Razavy type potential which transforms to single or double well potential according to negative or positive potential parameterk, is solved analytically by using extended form of Nikiforov-Uvarov (NU) method. It is presented that eigenvalue spectra of Schrodinger equation for this potential can be attained analytically by the method. Eigenfunction solutions that are depending on confluent Heun polynomials, are analyzed graphically for specified parameters.TUBITAKTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [118F245]The authors gratefully acknowledges TUBITAK for support with grant 118F245