Revisiting Dirac and Schr\"odinger: A Proof Offered for the Non-Relativistic Time-Dependent Schr\"odinger Equation

Abstract

In this paper, three plausible axioms together with two definitions are employed to build an axiomatic framework, and then with the help of the Dirac formalism, it is demonstrated that the time-dependent Schr\"odinger wave equation is no longer a postulate for the whole theory, but a theorem. Subsequently, a proof for the theorem is presented. The result implies that the other remaining axioms of the picture essentially involve the Schr\"odinger equation, and this consequence lets the whole theory become stronger.