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Birkhäuser Basel eBooks

Some Quantum Relations

Published Jan 1, 2009• 0 citations
Publisher

Abstract

Selected traditional quantum relations are discussed. The intention is roughly to complement a text connected to quantum dynamics with mathematical approaches to some quantum concepts; of course no exhaustive presentation should be expected and parallel reading of traditional books on quantum mechanics is highly recommended. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1007/978-3-7643-8795-2_15

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Chapter 2. Why is Quantum Relations Quantum?

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Selected traditional quantum relations are discussed. The intention is roughly to complement a text connected to quantum dynamics with mathematical approaches to some quantum concepts; of course no exhaustive presentation should be expected and parallel reading of traditional books on quantum mechanics is highly recommended. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Since this book is closely connected to quantum mechanics, these introductory words will briefly and informally recall some postulates of this theory. Interested readers are urged to consult traditional books on quantum mechanics to complement the discussion ahead and for descriptions of experimental evidence that give rise to the postulates. In physics there are several “equivalent formulations” of quantum mechanics, and a catalogue of the most important appears in [StyO2]. The discussion here is restricted to the nonrelativistic case.
This chapter gives an introduction to a chain of results attempting to exclude deeper layers underneath quantum mechanics that restore some form of classical physics: ‘[Such results] more or less illustrate the ways along which some opponents might hope to escape Bohr’s reasonings and von Neumann’s proof and the places where they are dangerously near breaking their necks.’ (Groenewold, 1946, p. 454). In so far as they are mathematically precise, such no-go results have their roots in von Neumann’s 1932 book, which gave rise to two traditions that were often in polemical opposition to each other. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.