Life and work
He studied in Berlin 1925-1933, changed due to the rise of the Nazis but at the Swiss Federal Institute of Technology Zurich (ETH Zurich ), where he worked with Wolfgang Pauli received his doctorate with Gregor Wentzel. Soon after, he emigrated to the USA where he became an assistant to Albert Einstein at the Institute for Advanced Study at Princeton. He studied with Einstein and Peter Bergmann five-dimensional Kaluza-Klein theories ( in Theodore von Karman Anniversary Volume 1941). During World War II he worked with John von Neumann shock wave problems and the numerical inversion of large matrices. From 1941 he taught at Princeton, where he became professor in 1946 and remained until his retirement.
With Eugene Wigner, he developed relativistic wave equations for particles of arbitrary spin. He also developed the theory of irreducible unitary representations of the Lorentz and Poincare ( where Wigner in 1939 pioneered ) and worked on the inverse scattering problem (reconstruction of the potential from the scattering phases). A Präzessionseffekt of particles in external electromagnetic fields is named after him, Louis Michel and Valentine Telegdi ( Bargmann -Michel- Telegdi equation, Physical Review Letters 1959). With Moshinsky he examined 1960/1961 the group theory of the harmonic oscillator in quantum mechanics. According to him, the Bargmann - rooms are named (sometimes Segal - Bargmann spaces to Irving Segal parallel development ), Hilbert spaces of holomorphic functions, which he studied from 1961.
For the number Nl of bound quantum states with angular momentum l in a rotationally symmetric potential he gave the upper limit
He was a talented pianist.