57 pp. Original printed wrappers, rebacked with new paper spine. Wrappers extensively remargined. Good. NOTE ABOUT PHOTOS: ABEBooks allows only 5 photos. I think these photos convey the extent of the restoration on this copy, but I can supply more photos of the restored wrappers, upon request. First Separate Printing. Pencil corrections in the text on pp. 27 and 45. I don't pretend to understand the following quotations, but they come from authoritative sources. Von Neumann "developed between 1927 [the paper offered here] and 1929 a new mathematical framework of the theory which subsequently proved to be the most suitable formalism of nonrelativistic quantum mechanics as we use it today [1966], as well as of its extensions, the relativistic quantum mechanics of particles and the quantum theory of fields" (Max Jammer, The Conceptual Development of Quantum Mechanics, pp. 314-315. "Von Neumann's most famous work in theoretical physics is his axiomatization of quantum mechanics. When he began work in that field in 1927 [in the paper offered here], the methods used by its founders were hard to formulate in precise mathematical terms: 'operators' on 'functions' were handled without much consideration of their domain of definition or their topological properties and it was blithely assumed that such 'operators,' when self-adjoint, could always be 'diagonalized' (as in the 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 points of a Hilbert space and that the measurable quantities were Hermitian (generally unbounded) operators densely defined 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 basis 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" (J. Dieudonné, in D.S.B. 14: 91). The D.S.B. is the Dictionary of Scientific Biography, a magnificent reference work in 18 volumes.
