The book Mathematical Foundations of Quantum Mechanics (1932) by John von Neumann is an important early work in the development of quantum theory. [1]
The book was originally published in German in 1932 by Julius Springer, under the title Mathematische Grundlagen der Quantenmechanik. [2] An English translation by Robert T. Beyer was published in 1955 by Princeton University Press. A Russian translation, edited by N. Bogolyubov, was published by Nauka in 1964. A new English edition, edited by Nicholas A. Wheeler, was published in 2018 by Princeton University Press. [3]
The book mainly summarizes results that von Neumann had published in earlier papers. [4] [5] [6] [7] [8] Its main significance may be its argument against the idea of hidden variables, on thermodynamic grounds. However, this idea was refuted as early as 1935 by Grete Hermann, but the critique remained unknown until J.S. Bell's rediscovery in 1966 [9] .
von Neumann's claim rested on the assumption that any linear combination of Hermitian operators represents an observable and the expectation value of such combined operator follows the combination of the expectation values of the operators themselves. [9] Bell shows that the consequences of that assumption are at odds with results of incompatible measurements, which are not explicitly taken into von Neumann's considerations.
Gerhard Karl Erich Gentzen was a German mathematician and logician. He made major contributions to the foundations of mathematics, proof theory, especially on natural deduction and sequent calculus. He died of starvation in a Czech prison camp in Prague in 1945, having been interned as a German national after the Second World War.
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Hermann Minkowski was a mathematician and professor at Königsberg, Zürich and Göttingen, described variously as German, Polish, or Lithuanian-German, or Russian. He created and developed the geometry of numbers and used geometrical methods to solve problems in number theory, mathematical physics, and the theory of relativity.
Hilbert's sixth problem is to axiomatize those branches of physics in which mathematics is prevalent. It occurs on the widely cited list of Hilbert's problems in mathematics that he presented in the year 1900. In its common English translation, the explicit statement reads:
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Grete Hermann was a German mathematician and philosopher noted for her work in mathematics, physics, philosophy and education. She is noted for her early philosophical work on the foundations of quantum mechanics, and is now known most of all for an early, but long-ignored critique of a "no hidden-variables theorem" by John von Neumann. It has been suggested that, had her critique not remained nearly unknown for decades, the historical development of quantum mechanics might have been very different.
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Eberhard Frederich Ferdinand Hopf was a German mathematician and astronomer, one of the founding fathers of ergodic theory and a pioneer of bifurcation theory who also made significant contributions to the subjects of partial differential equations and integral equations, fluid dynamics, and differential geometry. The Hopf maximum principle is an early result of his (1927) that is one of the most important techniques in the theory of elliptic partial differential equations.
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The Göttingen Academy of Sciences is the oldest continuously existing institution among the eight scientific academies in Germany, which are united under the umbrella of the Union of German Academies of Sciences and Humanities. It has the task of promoting research under its own auspices and in collaboration with academics in and outside Germany. It has its seat in the university town of Göttingen. Its meeting room is located in the auditorium of the University of Göttingen.
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This is a bibliography of works by Theodore von Kármán.
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