VON NEUMANN, JOHANN. [JOHN].

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).

Order-nr.: 49090