Revisiting the postulates of quantum mechanics

Abstract

This work reviews the fundamental postulates of quantum mechanics, in line with standard educational texts. The postulates provide the framework for the theory, starting with the properties of wave functions acceptable in the Schrödinger equation: uniqueness, continuity, and finiteness. This is followed by the introduction of quantum-mechanical operators that define the properties of quantum systems. The calculation of average values of observables is determined by the third postulate, and the fourth postulate addresses the Schrödinger equation in both its time-dependent and time-independent forms, as well as its extension to complex systems. Finally, the concept of spin and its properties are included. Contrary to the traditional order of presentation, this study suggests initiating the exploration of the postulates with the Schrödinger equation, reflecting the possible historical development of quantum mechanics and potentially enhancing conceptual understanding of the theory.