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Wahrscheinlichkeitstheoretischer Aufbau der Quantenmechanik; Thermodynamik quantenmechanischer Gesamtheiten.
Gesellschaft der Wissenschaften zu Göttingen, Berlin 1927 - Rare offprint issues, with distinguished provenance, of these two major papers in which Von Neumann laid out his probability-theoretic construction of quantum mechanics and founded the field of quantum thermodynamics. "That von Neumann has been ‘par excellence’ the mathematician of quantum mechanics is as obvious to every physicist now as it was a quarter of a century ago. Quantum mechanics was very fortunate indeed to attract, in the very first years after its discovery in 1925, the interest of a mathematical genius of von Neumann’s stature. As a result, the mathematical framework of the theory was developed and the formal aspects of its entirely novel rules of interpretation were analyzed by one single man in two years time (1927-1929). Conversely, one could almost say in reciprocity, quantum mechanics introduced von Neumann into a field of mathematical investigation, operator theory, in which he achieved some of his most prominent successes."In the course of his formulation of quantum mechanics in terms of vectors and operators of Hilbert space von Neumann also gave in complete generality the basic statistical rule of interpretation of the theory. This rule concerns the result of the measurement of a given physical quantity on a system in a given quantum state and expresses its probability distribution by means of a simple and now completely familiar formula involvingthe vector representing the state and the spectral resolution of the operator which represents the physical quantity. This statistical rule, originally proposed by Born in 1926, was for von Neumann the starting point of a mathematical analysis of quantum mechanics in entirely probabilistic terms. The analysis, carried out in a paper of 1927 [citing the first offered paper], introduced the concept of statistical matrix for the description of an ensemble of systems which are not necessarily all in the same quantum state. The statistical matrix (now often called ?-matrix although von Neumann’s notation was U) has become one of the major tools of quantum statistics and it is through this contribution that von Neumann’s name became familiar to even theleast mathematically minded physicists. "In the same paper von Neumann also investigates a problem which is still now the subject of much discussion, viz., the theoretical description of the quantum-mechanical measuring process and of the noncausal elements which it involves. Mathematically speaking vonNeumann’s study of this delicate question is quite elegant. It provides a clear-cut formal framework for the numerous investigations which were needed to clarify physically the all-important implications of quantum phenomena for the nature of physical measurements, the most essential of which is Niels Bohr’s concept of complementarity."The results of the paper just discussed were immediately used by the author to lay the foundation for quantum thermodynamics [citing the second offered paper]." (Léon Van Hove, Von Neumann’s Contributions to Quantum Theory.)Provenance: front wrappers with the signature of mathematician Aurel Friedrich Wintner (1903–1958) who did important work in probability theory and is considered one of the founders of probabilistic number theory. Two offprints from the Nachrichten der Gesellschaft der Wissenschaften zu Göttingen. Both 8vo (241 x 168 mm), in the original light green printed wrappers (some chipping and a few small tears to the extremeties), pp. [2:seperate title], [245] 246-272 [2:blank]; pp. [273] 274-291 [1:blank]. Very rare. [Attributes: First Edition]
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Last Found On: 2013-09-16           Check availability:      AbeBooks    

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