Valentine Bargmann

Valentine Bargmann , called Valya Bargmann, (born April 6, 1908 in Berlin , † July 20, 1989 in Princeton ) was a German-born American mathematical physicist and mathematician with Russian roots.

life and work

He studied in Berlin from 1925 to 1933, but switched to the Swiss Federal Institute of Technology in Zurich (ETH Zurich) when the National Socialists seized power , where he worked with Wolfgang Pauli and did his doctorate with Gregor Wentzel . Soon afterwards he emigrated to the USA , where he became Albert Einstein's assistant at the Institute for Advanced Study in Princeton . He investigated five-dimensional Kaluza-Klein theories with Einstein and Peter Bergmann (in Theodore von Karman Anniversary Volume 1941). During World War II he worked with John von Neumann on shock wave problems and the numerical inversion of large matrices. From 1941 he taught at Princeton , where he became a professor in 1946 and stayed until his retirement.

With Eugene Wigner , he developed relativistic wave equations for particles of any spin. He also developed the theory of the irreducible unitary representations of the Lorentz and Poincare groups (where Wigner did pioneering work in 1939) and worked on the inverse scattering problem (reconstruction of the potential from the scattering phases). A precession effect of particles in external electromagnetic fields is named after him, Louis Michel and Valentine Telegdi ( Bargmann-Michel-Telegdi equation , Physical Review Letters 1959). With Marcos Moshinsky he investigated the group theory of the harmonic oscillator in quantum mechanics in 1960/1961. The Bargmann spaces are named after him (sometimes also Segal-Bargmann spaces after Irving Segal's parallel development), Hilbert spaces of holomorphic functions, which he investigated from 1961.

He gave the upper limit for the number N _{l of} bound quantum mechanical states with angular momentum l in a rotationally symmetrical potential

${\displaystyle N_{l}\leq {\frac {1}{2l+1}}{\frac {2m}{\hbar ^{2}}}\int _{0}^{\infty }r|V(r)|dr}$

to (Proceedings National Academy 1952). Before that, Abraham Pais and Res Jost showed that no bound state exists if the integral is less than 1.

He was a talented pianist.

In 1968 he became a member of the American Academy of Arts and Sciences . In 1978 he and Eugene Wigner received the first Wigner Medal. In 1979 he was elected to the US National Academy of Sciences . In 1988 he received the Max Planck Medal .

Fonts (selection)

• Bargmann Irreducible unitary representations of the Lorentz group , Annals of Mathematics, Vol. 48, 1947, p. 568
• ders. On unitary representations of continuous groups , Annals of Mathematics Vol. 59, 1954, p. 1
• ders. On the connection between phase shift and scattering potential , Reviews of Modern Physics, Vol. 21, 1949, p. 488
• ders. On representations of the rotation group , Reviews of Modern Physics 1962
• id. a wizard memories Einstein , Quarterly magazine of Natural History Society in Zurich, Vol. 124, Issue 1, 1979
• V. Bargmann, EP Wigner: Group Theoretical Discussion of Relativistic Wave Equations. In: Proceedings of the National Academy of Sciences . Volume 34, Number 5, May 1948, pp. 211-223, PMID 16578292 , PMC 1079095 (free full text).
• V. Bargmann: On the Number of Bound States in a Central Field of Force. In: Proceedings of the National Academy of Sciences . Volume 38, Number 11, November 1952, pp. 961-966, PMID 16589209 , PMC 1063691 (free full text).
• V. Bargmann: Remarks on a Hilbert space of analytic functions. In: Proceedings of the National Academy of Sciences . Volume 48, Number 2, February 1962, pp. 199-204, PMID 16590920 , PMC 220756 (free full text).

literature

• Elliott H. Lieb , Barry Simon , Arthur Strong Wightman (Eds.) Studies in mathematical physics- Essays in honor of Valentine Bargmann , Princeton University Press 1976

Web links

• John R. Klauder: Valentine Bargmann 1908-1989 . In: National Academy of Sciences (Ed.): Biographical Memoirs . 1999 (English, nasonline.org [PDF]).
• V. Bargmann. In: Physics History Network. American Institute of Physics
• William Aspray, Albert Tucker: Transcript of an interview with Bargmann. In: The Princeton Mathematics Community in the 1930s. The Trustees of Princeton University, 1985 (English).