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‎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.‎