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Conference on the Foundations of Quantum Mechanics: Historical Analysis and Open Questions

AN OUTLINE OF AN INTERPRETATION OF QUANTUM MECHANICS

Gennaxo AULETTA

Published May 1, 2000• 16 citations
Publisher

Abstract

The main thesis of this article is that Quantum Mechanics consists in the Basic formalism (Schrödinger equation) plus the Measurement theory (or the theory of open systems).
DOI
10.1142/9789812793560_0002

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Our purpose in this chapter is to present the key concepts of quantum mechanics in the language of Hilbert spaces. The reader who has not previously met the physical ideas motivating quantum mechanics, and some of the more elementary applications of Schrödinger's equation, is encouraged to read any of a number of excellent texts on the subject such as [1–4]. Otherwise, the statements given here must to a large extent be taken on trust – not an altogether easy thing to do, since the basic assertions of quantum theory are frequently counterintuitive to anyone steeped in the classical view of physics. Quantum mechanics is frequently presented in the form of several postulates, as though it were an axiomatic system such as Euclidean geometry. As often presented, these postulates may not meet the standards of mathematical rigour required for a strictly logical set of axioms, so that little is gained by such an approach. We will do things a little more informally here. For those only interested in the mathematical aspects of quantum mechanics and the role of Hilbert space see [5–8]. Many of the standard applications, such as the hydrogen atom, will be omitted here as they can be found in all standard textbooks, and we leave aside the enormous topic of measurement theory and interpretations of quantum mechanics. This is not to say that we need be totally comfortable with quantum theory as it stands. Undoubtedly, there are some philosophically disquieting features in the theory, often expressed in the form of socalled paradoxes.
This article – introduction to the structural theory of general view dynamical systems, based on construction of dynamic quantum models (DQM), offered by the author. This model is simply connected with traditional model of quantum mechanics (i.e. with the Schrodinger equation). At the same time obtained thus non – Hamiltonian quantum dynamics is easier than classical one: it allow building the clear structural theory and effective algorithms of research for concrete systems. This article is devoted mainly to such task. The algorithm of search for DQM attractors, based on this approach, is offered here.