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

by

**Evert Jan Post**
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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