Analytical solution of D-dimensional radial Schrödinger equation for sextic potential by the extended Nikiforov–Uvarov method and biconfluent Heun polynomials

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 alsopresented that the D-dimensional radial SE is transformed to biconfluent Heun equation (BHE). Therefore the eigenfunctionsolutions for the potential are attained in terms of biconfluent Heun polynomials when the condition of existenceof polynomial solution of BHE is provided simultaneously.