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"VON NEUMANN, JOHANN (JOHN). - THE MATHEMATICAL FOUNDATION OF QUANTUM MECHANICS.
Reference : 47068
(1928)
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.
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).
Beweis des Ergodensatzes und des H-Theorems in der neuen Mechanik.
Berlin, Springer, 1929. 8vo. In contemporary half cloth with gilt lettering to spine. In ""Zeitschrift für Physik"", bd. 57, 1929. Entire issue offered. Library stamp to front free end-paper and light wear to spine, otherwise fine and clean. Pp. 30-70. [Entire volume:VII, (1), 872 pp.].
First printing of Neumann's important formulation and proof of an ergodic theorem for quantum systems.""The basic principle of this work is to define quantum analogues of cells in phase space by considering sets of quantum states for which all macroscopic quantities have given values within a certain inaccuracy. One further considers the unitary transformation u relating these quantum states to the eigenstates of the hamiltonian. The ergodicity is then established for ""almost every"" value of the transformation u. Although the latter restriction is a rather unsatisfactory one from the physical standpoint, one must consider von Neumann's ergodic theorem as one of the very few important contributions to a most difficult subject which even now is far from complete clarification."" (Hove, Von Neumann's Contributions to Quantum Theory, p. 98).
Eine Axiomatisierung der Mengenlehre. [In: Journal für die reine und angewandte Mathematik, vol. 154, pp.219-240]. - [THE VON NEUMANN AXIOMS OF SET THEORY]
Berlin & Leipzig: Walter de Gruyter, 1925. Large 4to. (300x234mm). The entire volume 154 [(4),259,(1) pp.] offered here in original blank wrappers. Exceptionally fine.
![Eine Axiomatisierung der Mengenlehre. [In: Journal für die reine und angewandte Mathematik, vol. 154, pp.219-240]. - [THE VON NEUMANN AXIOMS OF SET ...](https://static.livre-rare-book.com/pictures/LLX/38042_1_thumb.jpg)
![Eine Axiomatisierung der Mengenlehre. [In: Journal für die reine und angewandte Mathematik, vol. 154, pp.219-240]. - [THE VON NEUMANN AXIOMS OF SET ...](https://static.livre-rare-book.com/pictures/LLX/38042_2_thumb.jpg)
First edition of von Nuemann's first significant publication, in which he introduced the concept of classes, and gave the first finite axiomatisation of set theory.
NEUMANN, JOHANN (JOHN) von. - THE MATHEMATICAL FOUNDATION OF QUANTUM PHYSICS.
Reference : 53414
(1932)
Mathematische Grundlagen der Quantenmechanik. Mit 4 Abbildungen.
Berlin, Springer, 1932. 8vo. Orig. full yellow cloth. with orig. printed dustjacket. Jacket with a few minor small tears. Small stamp on titlepage and jacket with previous owners name: Niels Arley (1911-94, collaborated with Niels Bohr, professor at Inst. of Theoretical Physics, Univ. of Copenhagen). (8),262,(2) pp. With many annotations in small pencil by Niels Arley throughout.
First edition. In the early years of quantum mechanics several distinct formulations were developed Heisenberg's matrix mechanics, Schrödinger's wave mechanics, and Dirac's more general transformation theory. However these theories lacked strict mathematical rigor (only much later through Schwartz's theory of distributions did Dirac's theory achieve this). Quantum mechanics is one of the fields of science which was fortunate to attract the attention of a mathematician of von Neumann's character. Von Neumann showed, in a paper published 1927, how generalized infinite-dimensional Euclidean spaces (function spaces) and linear operators provide the proper mathematical framework for quantum mechanics. Von Neumann was strongly influenced by Hilbert's program of axiomatizing the fields of science. The axiomatic approach which von Neumann takes in his theory has ever since dominated modern physics and functional analysis, and it was von Neumann who coined the term 'Hilbert space'. Von Neumann's work in this field culminated in this monograph which in addition to the earlier paper includes his important considerations, inspired by Bohr and Heisenberg, regarding the problem of measurement, in particular von Neumann's disproof of hidden variables.
