‎"VON NEUMANN, JOHANN (JOHN). - THE MATHEMATICAL FOUNDATION OF QUANTUM MECHANICS.‎
‎Mathematische Grundlagen der Quantenmechanik. (+) Wahrscheinlichkeitstheoretischer Aufbau der Quantenmechanik. (+) Thermodynamik quantenmechanischer Gesamtheiten. (3 Papers).‎

‎Berlin, Weidmannsche Buchhandlung, 1928. 8vo. Full cloth, but spine gone. In: ""Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen aus dem Jahre 1927"". (4),469 pp. Von Neumann's papers: pp. 1-57, pp. 245-272 a. pp. 273-291. Internally clean and fine.‎

Reference : 47068

‎First printing of von Neumann's importent papers in which he gave a mathematically precise formulation of the foundation of Quantum MeChanics, basing the theory on the use of Hilbert spaces.""He (von Neumann) developed between 1927 and 1929 a new mathematical framework of the theory subsequently proved to be the most suitable formalism of nonrelativistic quantum mechanics as we use it today, as well as of its extensions, the relativistic quantum mechanics of partcles and the quantum theory of fields.""(Max Jammer ""The Conceptual Development og Quantum Mechanics"", pp.314-15""Von Neumann’s most famous work in theoretical physics is his axiomatization of quantum mechanics. When he began work in that field in 1927, the methods used by its founders were hard to formulate in precise mathematical terms"" ""operator"" on ""functions"" were handled without much consideration of their domain or definition to their topological properties: and it was blithely assumed that such ""operators,"" when self-adjoint, could always be ""diagonalized"" (as in th finite dimensional case), at the expense of introducing ""Dirac functions"" as ""eigenvectors."" Von Neumann showed that mathematical rigor could be restored by taking as basic axioms the assumptions that the states of a physical system were poinds of a Hilbert space and that the measurable quantities were Hermitian (generally unbounded) operators densely efined in that space. This formalism. the practical use of which became available after von Neumann had developed the spectral theory of unbounded Hermitian operators (1929), has survived subsequent developments of quantum mechanics and is still the basisi of non relativistic quantum theory"" with the introduction of the theory of distributions, it has even become possible to interpret its results in a way similar to Dirac’s original intuition.""(DSB).‎