Barry Simon

Barry Martin Simon (born 16 April 1946) 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 (particularly Schrödinger operators), 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 (including N-body systems and resonances), 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, whose original surname was Slopak, adopted the surname Simon after immigrating to the United States. Simon attended James Madison High School in Brooklyn. Simon is an observant Jew. 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.

Honors and awards 1974: Invited Speaker at the International Congress of Mathematicians in Vancouver 1981: Elected fellow of the American Physical Society 1990: Elected correspondent member of the Austrian Academy of Sciences 2005: Elected fellow of the American Academy of Arts and Sciences 2012: Elected fellow of the American Mathematical Society 2012: Awarded the Henri Poincaré Prize 2016: Awarded the Steele Prize for Lifetime achievements 2019: Elected to the National Academy of Sciences

Selected publications Articles (over 700 citations)

(over 700 citations)

(over 1500 citations) (with M. Aizenman) Brownian motion and Harnack's inequality for Schrödinger operators, Commun. Pure Appl. Math. 35 (1982), 209–273 (over 600 citations) (over 2050 citations) (over 600 citations)

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 (Quantum) 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. online PDF; 377 kB. pp. 327–349: Quantum dynamics: from automorphism to hamiltonian. online PDF; 573 kB. Functional integration and quantum physics (= Pure and Applied Mathematics. 86). Academic Press, New York NY etc. 1979, ISBN 0-12-644250-9 (2nd edition: American Mathematical Society, Providence RI 2005, ). Trace Ideals and their applications (= London Mathematical Society. Lecture Note Series. 35). Cambridge University Press, Cambridge etc. 1979, (2nd edition: (= Mathematical Surveys and Monographs. 120). American Mathematical Society, Providence RI 2005, ). with Hans L. Cycon, Richard G. Froese, and Werner Kirsch: Schrödinger Operators. Springer, Berlin etc. 1987, (corrected and extended 2nd printing: Springer 2008, ). The Statistical mechanics of lattice gases. vol. 1. Princeton University Press, Princeton NJ 1993. Orthogonal polynomials on the unit circle (= American Mathematical Society Colloquium Publications. 54, 1–2). 2 vols. American Mathematical Society, Providence RI 2005; vol. 1: Classical theory. 2005, ; vol. 2: Spectral theory. 2005. Convexity. An analytic viewpoint (= Cambridge Tracts in Mathematics. 187). 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. A Comprehensive Course in Analysis. 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. Loewner's theorem on monotone matrix functions Springer, 2019,