A First Lecture on Quantum Mechanics

Abstract

In this paper we give, on an introductory level, a unified formulation of ‘quantum’ physics. The formalism which is obtained by taking seriously Einstein’s point of view and describe a physical system in terms of ‘elements of reality’, is presented in the spirit of what might be called the ‘school of Geneva’. The lecture is divided into four sections. First we introduce the notions of physical system, question and proposition, and show that the propositions are naturally embedded in a lattice. In the second section we discuss the propositional system, introducing the postulates of ‘quantum’ physics. Furthermore, we define the notion of state of a physical system. Next, we define what is meant by saying that two propositions are compatible and introduce some criteria for compatibility. We also consider some realizations of propositional systems, before ending the section by defining the concept of observable and justify the use of self-adjoint operators. The last section is devoted to a proof of the probability law of quantum mechanics, usually assumed as a postulate.