# Barry Simon

**Barry Martin Simon ** (born 16 April 1946) is an American mathematical physicist and the IBM Professor of Mathematics and Theoretical Physics at Caltech,^{[1]} 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.

Barry Simon | |
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Born | 16 April 1946 (age 73) |

Education | A.B., Harvard University Ph.D., Princeton University |

Employer | Caltech |

Title | Professor |

Spouse(s) | Martha Simon |

Awards | Henri Poincaré Prize (2012) Bolyai Prize (2015) Steele Prize (2016) |

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.

## Contents

## Early lifeEdit

Barry Simon's mother was a school teacher, his father was an accountant. Simon attended James Madison High School in Brooklyn.

## CareerEdit

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 A.B. in 1966 from Harvard College and his Ph.D. 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.

His status is legendary in mathematical physics and he is renowned for his ability to write scientific manuscripts "in five percent of the time ordinary mortals need to write such papers."^{[2]}

A former graduate student of Simon's, in a tale revealing of his brilliance, once stated:

Barry has always been remarkable for his vast knowledge of mathematics, so it was many years before I can recall ever telling him a published theorem he didn't already know. One day I saw Barry in Princeton shortly after a meeting and told him about an old inequality for PDEs, which, as I could tell from his intent look, was new to him. I said, "It seems to be useful. Do you want to see the proof?" His response "No, that's OK." Then he went to the board and wrote down a flawless proof on the spot.

^{[3]}

## Honors and awardsEdit

- 2012: Elected fellow of the American Mathematical Society.
^{[4]} - 2012: Awarded the Henri Poincaré Prize
- 2015: Awarded the Bolyai Prize of the Hungarian Academy of Sciences.
^{[5]} - 2016: Awarded the Steele Prize for Lifetime achievements.
- 2018: Dannie Heineman Prize for Mathematical Physics from the American Physical Society
^{[6]}

## Selected publicationsEdit

- Resonances in
*n*-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory, Annals of Mathematics 97 (1973), 247–274 - (with M. Reed) Methods of Modern Mathematical Physics, Vol. I: Functional Analysis, Academic Press, 1972; Vol. II: Fourier Analysis, Self-Adjointness, Academic Press, 1975; Vol. III: Scattering Theory, Academic Press, 1978; Vol. IV: Analysis of Operators, Academic Press, 1977
- (with F. Guerra and L. Rosen) The P(φ)
_{2}quantum theory as classical statistical mechanics, Annals of Mathematics 101 (1975), 111–259 - (with E. Lieb) The Thomas-Fermi theory of atoms, molecules and solids, Advances in Math. 23 (1977), 22–116
- (with J. Fröhlich and T. Spencer) Infrared bounds, phase transitions and continuous symmetry breaking, Commun. Math. Phys. 50 (1976), 79–85
- (with P. Perry and I. M. Sigal) Spectral analysis of multiparticle Schrödinger operators, Annals of Mathematics 114 (1981), 519–567
- (with M. Aizenman) Brownian motion and Harnack's inequality for Schrödinger operators, Commun. Pure Appl. Math. 35 (1982), 209–273
- Semiclassical analysis of low lying eigenvalues, II. Tunneling, Annals of Mathematics 120 (1984), 89–118
- Holonomy, the quantum adiabatic theorem and Berry's phase, Phys. Rev. Lett. 51 (1983), 2167–2170
- (with T. Wolff) Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians, Commun. Pure Appl. Math. 39 (1986), 75–90
- Operators with singular continuous spectrum: I. General operators, Annals of Mathematics 141 (1995), 131–145
*A Comprehensive Course in Analysis*, American Math Society, (2015)]

## ReferencesEdit

**^**Caltech Math Faculty page**^**"Simonfest Barry Stories: Jürg Fröhlich". math.caltech.edu.**^**"Simonfest Barry Stories: Evans Harrell". math.caltech.edu.**^**List of Fellows of the American Mathematical Society. Retrieved 2013-07-20.**^***Bolyai Prize goes to Barry Simon*Archived 2015-12-22 at the Wayback Machine Communication by Hungarian Academy of Sciences (mta.hu). Retrieved 12 April 2015**^**"Dannie Heineman Prize for Mathematical Physics". American Physical Society. Retrieved 7 September 2018.

## Further readingEdit

## External linksEdit

- Prof. Simon's Homepage
- SimonFest
- Gesztesy, Fritz (August 2016), "From Mathematical Physics to Analysis: A Walk in Barry Simon's Mathematical Garden" (PDF),
*Notices of the American Mathematical Society*, Providence, RI: American Mathematical Society,**63**(7): 740–752 - Gesztesy, Fritz (September 2016), "From Mathematical Physics to Analysis: A Walk in Barry Simon's Mathematical Garden, II" (PDF),
*Notices of the American Mathematical Society*, Providence, RI: American Mathematical Society,**63**(8): 878–889 - Barry Simon at the Mathematics Genealogy Project
- Publications and citations at Google Scholar