JORDAN-KLEIN MATRICES

JORDAN, PASCUAL (+) O. KLEIN.

Zum Mehrkörperproblem der Quantentheorie (+) Über Wellen und Korpuskeln in der Quantenmechanik.

Berlin, Julius Springer, 1927. 8vo. Entire volume 45 of "Zeitschrift für Physik" bound in contemporary half cloth with gilt title to spine. Library stamp to title-page. Corners and lower capital bumped, hinges a bit weak. An overall fine and clean copy. Pp. 751-765; 766-775. [Entire volume: VII, (1), 910 pp.].

First publication of Jordan and Klein's influential paper (the first mentioned) which contributed to the close connection between quantum fields and quantum statistics, today known as Jordan-Klein matrices.
"Born, Heisenberg, and Jordan had indicated, and Dirac had demonstrated, the close connection between quantum fields and quantum statistics. Second quantization guarantees that photons obey Bose-Einstein statistics. What about other particles which obey Bose-Einstein statistics? The year 1927 was not over before Jordan and Klein addressed this question [in the present paper]." (Pais, Inward bound. p. 338).
"Jordan and Klein found that "one can quantize just as well the non-relativistic Schroedinger equation. In honor of these contributions the matrices have been named Jordan-Klein matrices." (ibid. p. 339).

"Convinced that the many-body problem in quantum mechanics can be stated correctly only in the context of quantized matter waves ("repeated" or "second" quantization. as it was called later by Léon Rosenfeld), Jordan started working out his ideas together with Wolfgang Pauli. Oskar Klein, and Eugene Wigner. During his stay in Copenhagen in the summer 1927 Jordan established, together with Klein, the first nonrelativistic formalism of second quantization for a system of interacting Bose particles." (DSB).

The second paper, "Über Wellen und Korpuskeln in der Quantenmechanik", "contained several other formal and mathematical generalizations, but its main practical value is that, in the newly established theory of the 'quantized wave field', the fluctuations in the Bose case now satisfied all requirements following from Einstein's light-quantum treatment of 1924 and 1925." (Mehra, The historical development of quantum theory, 2000, p. 231.

Order-nr.: 49120