Lie Symmetries of Klein-Gordon and Schrödinger Equations

Abstract

In this paper, we investigate the Lie point symmetries of Klein-Gordon equation and Schrödinger equation by applying the geometric concept of Noether point symmetries for the below defined Lagrangian. Moreover, we organize a strong relationship among the Lie symmetries related to Klein-Gordon as well as Schrödinger equations. Finally, we utilize the consequences of Lie point symmetries of Poisson and heat equations within Riemannian space to conclude the Lie point symmetries of Klein-Gordon equation and Schrödinger equation within universal Riemannian space.