Title
Quantum Reprogramming: Ensembles and Single Systems: A TwoTier Approach to Quantum Mechanics (Boston Studies in the Philosophy ,New
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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 midThirties. 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 longstanding dichotomy by examining the mutual relation between single systems and ensembles, assigning each its own tools for treating the subject at hand: i.e., SchrdingerDirac 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 oldtime 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.
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