4 October 2002
NEUMANN, John von. Mathematische Grundlagen der Quantenmechanik. Berlin: Springer, 1932. 8o. Original cloth. Provenance: Milton Plesset (signature on front free endpaper). FIRST EDITION. -- Mathematical Foundations of Quantum Mechanics. Translated by Robert T. Beyer. Princeton: Princeton University Press, 1955. 8o. Original printed wrappers. FIRST EDITION, in English.
Von Neumann's axiomatization of quantum mechanics. "It was von Neumann's deep insight in 1926 that if he was to be the Lagrange of quantum mechanics, he might 'abstract out the essence of quantum theory' by use of the language and algebra of an infinitely dimensional space but make the abstract formulation itself independent of the choice of coordinate system, just as the relation between figures in Euclidean geometry is independent of any coordinate system. Such an abstract formulation would have to contain the Heisenberg and Schrödinger descriptions of quantum mechanics as particular representations. Moreover, it would be desirable to found the mathematical theory on strict axioms in the spirit of Hilbert's philosophy. These are the three streams that von Neumann joined in his Mathematical Foundations of Quantum Mechanics: physical quantum theory itself, axiomatics, and a powerful mathematical tool, the theory of infinite-dimensional spaces. The last was to reconcile the first two... Only von Neumann evolved a complete formulation [of quantum mechanics] that was fully rigorous. It ultimately proved itself to be a superb formalism for quantum mechanics and could in fact encompass later extensions of quantum theory" (Heims, John von Neumann and Norbert Wiener, pp. 109-115). See Mehra & Rechenberg, Hist. Dev. Quantum Theory, 3, pp. 122-23 (note).
[With]: Wahrscheinlichkeitstheoretischer Aufbau der Quantenmechnik. -- Thermodynamik quantenmechanischer Gesamtheiten. Both offprints from: Nachrichten der Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-Physikalische Klasse. 1927. Original printed wrappers. (4)
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