Nonrelativistic Solutions of Morse Potential from Relativistic Klein-Gordon Equation

Abstract

Recently it is suggested that it may be possible to obtain the approximate or exact bound state solutions of nonrelativistic Schrodinger equation from relativistic Klein-Gordon equation, which seems to be counter-intuitive. But the suggestion is further elaborated to propose a more detailed method for obtaining nonrelativistic solutions from relativistic solutions. We demonstrate the feasibility of the proposed method with the Morse potential as an example. This work shows that exact relativistic solutions can be a good starting point for obtaining nonrelativistic solutions even though a rigorous algebraic method is not found yet.