Eur. Phys. J. Plus (2016) 131: 35
https://doi.org/10.1140/epjp/i2016-16035-5

Regular Article

Cornell interaction in the two-body semi-relativistic framework: The Lie algebraic approach

¹ Department of Physics, University of Guilan, 41635-1914, Rasht, Iran
² Department of Basic Sciences, Garmsar Branch, Islamic Azad University, Garmsar, Iran

^* e-mail: t-panahi@guilan.ac.ir

Received: 13 November 2015
Accepted: 23 December 2015
Published online: 15 February 2016

Abstract

We consider an approximation to the two-body spinless Salpeter equation which is valid for the case of heavy quarks with the Cornell potential. We then replace the square of kinetic term with its nonrelativistic equivalent and obtain an equation which can be alternatively viewed as the generalization of the Schrödinger equation into the relativistic regime. In the calculations, we use the Lie algebraic approach within the framework of quasi-exact solvability. With the help of the representation theory of , the ( -dimensional matrix equation of the problem is constructed in a quite detailed manner and thereby the quasi-exact expressions for the energy eigenvalues and the corresponding wave functions as well as the allowed values of the potential parameters are obtained.