Proof of the ergodic theorem and the H-theorem in quantum mechanics*
Translation of: Beweis des Ergodensatzes und des H-Theorems in der neuen Mechanik
Revised: 30 June 2010
Published online: 30 September 2010
It is shown how to resolve the apparent contradiction between the macroscopic approach of phase space and the validity of the uncertainty relations. The main notions of statistical mechanics are re-interpreted in a quantum-mechanical way, the ergodic theorem and the H-theorem are formulated and proven (without “assumptions of disorder”), followed by a discussion of the physical meaning of the mathematical conditions characterizing their domain of validity.
The German original was published in Zeitschrift für Physik 57, 30–70 (1929) [paper received on May 10th, 1929] and is available as electronic supplementary material at www.epj.org. Translated by Roderich Tumulka, Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA; e-mail: email@example.com. Additions in the text by the translator are put in square brackets. Footnotes are also footnotes in the original unless otherwise marked. Footnotes in the original containing only citations have been moved to the main text. In the original, equations and references are not numbered. The notation agrees essentially with the original, with the following exceptions: h/2π has been replaced with ħ; the notation [a,b] for intervals has been introduced to simplify some sentences. In a few cases, misprints and other mistakes in formulas have been identified by the translator, corrected in the text, and mentioned in a footnote. The translator is grateful to Wolf Beiglböck for suggesting improvements and librarian Mei Ling Lo of Rutgers University for help with the bibliography.
© EDP Sciences, Springer-Verlag 2010