Barry Simon


Barry Martin Simon is an American mathematical physicist and was the IBM professor of Mathematics and Theoretical Physics at Caltech, known for his prolific contributions in spectral theory, functional analysis, and nonrelativistic quantum mechanics, including the connections to atomic and molecular physics. He has authored more than 400 publications on mathematics and physics.
His work has focused on broad areas of mathematical physics and analysis covering: quantum field theory, statistical mechanics, Brownian motion, random matrix theory, general nonrelativistic quantum mechanics, nonrelativistic quantum mechanics in electric and magnetic fields, the semi-classical limit, the singular continuous spectrum, random and ergodic Schrödinger operators, orthogonal polynomials, and non-selfadjoint spectral theory.

Early life

Barry Simon's mother was a school teacher, his father was an accountant. His ancestors were from Odesa and Grodno. His grandfather got the new surname, Simon, at Ellis Island; his original surname was Slopak. Simon attended James Madison High School in Brooklyn. Simon is an observant Jew.

Career

During his high school years, Simon started attending college courses for highly gifted pupils at Columbia University. In 1962, Simon won a MAA mathematics competition. The New York Times reported that in order to receive full credits for a faultless test result he had to make a submission with MAA. In this submission he proved that one of the problems posed in the test was ambiguous.
In 1962, Simon entered Harvard with a stipend. He became a Putnam Fellow in 1965 at 19 years old. He received his AB in 1966 from Harvard College and his PhD in Physics at Princeton University in 1970, supervised by Arthur Strong Wightman. His dissertation dealt with Quantum mechanics for Hamiltonians defined as quadratic forms.
Following his doctoral studies, Simon took a professorship at Princeton for several years, often working with colleague Elliott H. Lieb on the Thomas–Fermi Theory and Hartree–Fock Theory of atoms in addition to phase transitions and mentoring many of the same students as Lieb. He eventually was persuaded to take a post at Caltech, from which he retired in the summer of 2016.

Honors and awards

Articles

  • , Commun. Pure Appl. Math. 35, 209–273

  • Books

  • Quantum mechanics for hamiltonians defined as quadratic forms. Princeton University Press, Princeton NJ 1971,.
  • with Michael C. Reed: Methods of Modern Mathematical Physics. 4 vols. Academic Press, New York, NY etc. 1972–1978;
  • * vol. 1: Functional Analysis. 1972, ;
  • * vol. 2: Fourier Analysis, Self-Adjointness. 1975, ;
  • * vol. 3: Scattering Theory. Academic Press, 1979, ;
  • * vol. 4: Analysis of Operators. Academic Press, 1978,.
  • The Euclidean Field Theory. Princeton University Press, Princeton NJ 1974,.
  • as editor with Elliott H. Lieb and Arthur S. Wightman: Studies in mathematical physics. Essays in Honor of Valentine Bargmann. Princeton University Press, Princeton NJ 1976,, contributions by Barry Simon:
  • * pp. 305–326: On the number of bound states of two body Schrödinger operators – a review.
  • * pp. 327–349: Quantum dynamics: from automorphism to hamiltonian.
  • Functional integration and quantum physics. Academic Press, New York NY etc. 1979, ISBN 0-12-644250-9.
  • Trace Ideals and their applications. Cambridge University Press, Cambridge etc. 1979, .
  • with Hans L. Cycon, Richard G. Froese, and Werner Kirsch: Schrödinger Operators. Springer, Berlin etc. 1987, .
  • The Statistical mechanics of lattice gases. vol. 1. Princeton University Press, Princeton NJ 1993,.
  • Orthogonal polynomials on the unit circle. 2 vols. American Mathematical Society, Providence RI 2005;
  • * vol. 1: Classical theory. 2005, ;
  • * vol. 2: Spectral theory. 2005,.
  • Convexity. An analytic viewpoint. Cambridge University Press, Cambridge etc. 2011,.
  • Szegő´s theorem and its descendants. Spectral theory for perturbations of orthogonal polynomials. Princeton University Press, Princeton NJ 2011,.
  • . 4 vols. with vol. 2 published in 2 parts, American Mathematical Society, Providence RI 2015,.
  • * vol. 1: Real Analysis.
  • * vol. 2A: Basic Complex Analysis.
  • * vol. 2B: Advanced Complex Analysis.
  • * vol. 3: Harmonic Analysis.
  • * vol. 4: Operator Theory.
  • Springer, 2019,