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The motion of a nucleon in q-deformed Eckart potential field coupled with Yukawa-type tensor potential is described by using Dirac equation. The bound state solutions of Dirac equation for q-deformed Eckart potential with Yukawa-type tensor potential under exact spin- and pseudospin-symmetric limit are obtained using finite Romanovski polynomials. The approximate relativistic energy spectra are exactly obtained within the approximation scheme of centrifugal term. The relativistic energy is negative for pseudospin symmetry and positive for spin symmetry. The radial component of Dirac spinors are obtained in terms of Romanovski polynomials under exact spin- and pseudospin-symmetric conditions. The relativistic energy spectrum for the exact spin-symmetric case reduces to non-relativistic energy spectrum in the non-relativistic limit. Received: 23 October 2013; Revised: 02 November 2013 Accepted: 10 November 2013

The energy eigenvalues and eigenfunctions of Schrodinger equation for Modified Poschl-Teller potential plus trigonometric Rosen-Morse non-central potential are investigated approximately in terms of finite Romanovski polynomial. The approximation has been made to solve the radial Schrodinger equation. The approximate bound state energy eigenvalues are given in a closed form and corresponding radial and eigenfunctions are obtained in terms of Romanovski polynomials. The polar eigenfunctions are obtained in terms of Romanovski polynomials. The trigonometric Rosen-Morse potential is considered to be perturbation factor to the modified Poschl-Teller potential since it causes the decrease of the length of angular momentum vectors.

A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schrodinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established. The map is constructed by reworking the Rodrigues formula in an elementary and natural way. The generating function is summed in closed form from which recursion relations and addition theorems follow. Relations to some classical polynomials are also given.

The energy eigenvalues and eigenfunctions of Schrodinger equation for Hulthen potential plus Eckart potential with the centrifugal term are investigated approximately in terms of finite Romanovski polynomial. The bound state energy eigenvalues are given in a closed form and corresponding eigenfunctions are obtained in terms of Romanovski polynomials.

In this paper, we apply a simple transformation method to construct exactly solvable potentials of Schrodinger equation in any arbitrary dimensional Euclidean space. The normalized wave functions of the constructed potentials are obtained in terms of Romanovski polynomials.