Ensembles and Single Systems: A Two-Tier Approach to Quantum Mechanics

BOSTON STUDIES IN THE PHILOSOPHY OF SCIENCE
Volume 181

Many, perhaps most textbooks of quantum mechanics present a
Copenhagen, single system angle; fewer present the subject matter as an instrument for treating ensembles, but the two methods have been silently coexisting since the mid-Thirties. This lingering dichotomy of purpose for a major physical discipline has much shrouded further insights into the foundations of quantum theory.

Quantum Reprogramming resolves this long-standing dichotomy by examining the mutual relation between single systems and ensembles, assigning each its own tools for treating the subject at hand: i.e., Schroedinger-Dirac methods for ensembles versus period
integrals for single systems.

A unified treatment of integer and fractional quantum Hall effects and a finite description of the electron's anomalies are mentioned as measures of justification for the chosen procedure of resolving an old-time dichotomy. The methods of presentation are, in part, elementary, with repetitive references needed to delineate differences with respect to standard methods. The parts on period integrals are developed with a perspective on elementary methods in physics, thus leading up to some standard results of de Rham theory and algebraic topology.

Audience: Students of physics, mathematics, philosophers as well as outsiders with a general interest in the conceptual development of physics will find useful reading in these pages, which will stimulate further inquiry and study.

Kluwer Academic Publishers, Dordrecht
Hardbound, ISBN 0-7923-3565-1
July 1995, 332 pp.

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