Quantum reprogramming

Many, perhaps most textbooks present a Copenhagen single system angle on quantum mechanics, fewer present the subject matter as an instrument for treating ensembles. 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. This collection of essays is an attempt at resolving this long standing dichotomy by examining the mutual relation of single systems and ensembles by 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.