Derivation of Both Klein-Gordon Equation and Time Dependent Schrdinger Equation From Classical Wave Function

Abstract

In this study, both of Klein-Gordon equation and time dependent Schrdinger equation are directly derived from De Broglie hypothesis (? = h=p). Besides that, a new formula of Klein- ordon equation was obtained by used two equations, i.e., the classical wave function and relativistic total energy relation hw = (h2k2)=2m+V ?. Moreover, a new equation of time dependent Schrdinger (TDSE) in three-dimension 3D was derived and evidently obtained. Thus, previous result is corresponding to (TDSE) in 3D calculated by using two equations, (i.e., Einstein energy and Newton second law of mechanics).