Foundations of quantum mechanics (II): equilibrium, Bohr–Sommerfeld rules and duality

Abstract

The present paper is divided into two parts. In the first part we present a new axiomatic derivation of the Schrödinger equation from three basic postulates. This new derivation sheds some light on the statistical character of the quantum formalism. We also show the formal connection between this derivation and the one done by other means in paper I of this series. The role of the entropy in all these developments is discussed at length. A discussion about the wave-particle duality problem is also presented. It is shown that the present approach avoids this problem. In the second part we show how to derive the Bohr–Sommerfeld quantization rules from the infinitesimal Wigner–Moyal transformation of paper I. We will thus show to what extent these rules are constituent of the modern quantum formalism and interpretation. The Feynman path integral formalism will also be derived from some slight modification of this approach, thus providing a high level of formal unification for our developments. These results will then be applied to provide fully corpuscular explanations of diffraction and interference experiments. When connecting these applications to the developments of the first part we will be able to exemplify quite clearly in what sense the duality problem is avoided by the present approach.