Derivation of both Klein-Gordon equation and Time Dependent Schrödinger Equation form classical wave function

Abstract

In this study, both the Klein-Gordon equation and time-dependent Schrodinger equation are directly derived from De Broglie's  (\lamda=h/p). Besides that, a new formula of the Klein-Gordon equation was obtained by using two equations, i.e., the classical wave function and relativistic total energy relation [[hw] = [(h^2 k^2)/2m] + V]. Moreover, a new equation of time-dependent Schrodinger (TDSE) in three-dimension 3D was derived and evidently obtained. Thus, the previous result corresponds to (TDSE) in 3D calculated using two equations, (i.e., Einstein energy and Newton's second law of mechanics).