Analytical solution of D-dimensional radial Schrödinger equation for sexticpotential by the extended Nikiforov-Uvarov method and biconfluent Heunpolynomials

Abstract

D-dimensional radial Schrödinger equation (SE) for sextic potential is solved using the extended Nikiforov-Uvarov method analytically. Energy eigenvalue and eigenfunction solutions are achieved systematically. It is also presented that the D-dimensional radial SE is transformed to biconfluent Heun equation (BHE). Therefore the eigenfunction solutions for the potential are attained in terms of biconfluent Heun polynomials when the condition of existence of polynomial solution of BHE is provided simultaneously.