Exact solutions of the Klein–Gordon equation with Makarov potential and a recurrence relation

Abstract

In this paper, the Klein–Gordon equation with equal scalar and vector Makarov potentials is studied by the factorization method. The energy equation and the normalized bound state solutions are obtained, a recurrence relation between the different principal quantum number n corresponding to a certain angular quantum number ℓ is established and some special cases of Makarov potential are discussed.