A Proper Quantization Rule for Solving the Klein-Gordon Equation with Equal and Unequal Scalar and Vector Interaction Potentials

Abstract: Based on the formal equivalence between the non-relativistic Schrödinger equation and the relativistic Klein-Gordon equation and using the proper quantization rule as well as the Riccati equation solution, exact solutions are established for a set of interaction potentials (second Rosen-Morse, Pöschl-Teller, second Pöschl-Teller, Scarf II, and Eckart hyperbolic type potentials). The calculations are elaborated in the case of equal scalar and vector potentials. The general case of unequal scalar-vector potentials is detailed for the case of harmonic potential class. Keywords: Proper quantization rule, Exact solutions, Klein-Gordon equation, Riccati equation. PACS number: 03.65.Ge; 03.65.Fd; 03.65.Bz; 03.65.−w.