Carl Bender

Konneker Distinguished Professor Emeritus of Physics
PhD, Harvard University
AM, Harvard University
AB, Cornell University
research interests:
  • Theoretical & Mathematical Physics
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    • MSC 1105-109-03
    • ST. LOUIS, MO 63130-4899
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    Professor Bender's scholarly expertise is in mathematical physics and applied mathematics. He is recognized as an expert on the subject of asymptotic analysis, differential equations, and perturbative methods and their use in solving problems of theoretical physics.

    Carl Bender applies the tools of applied mathematics to solve problems in mathematical physics. His past work includes (i) pioneering research on the anharmonic oscillator and studies of coupling-constant analyticity; (ii) development of the field of perturbation theory in large order, (iii) strong-coupling, finite-element, and mean-field approximations in quantum field theory, (iv) development of the field of PT-symmetric quantum mechanics. He has served as the coach at Washington University for the Putnam Mathematical Competition for many years.


    Professional History

    Postdoctoral Fellow, Institute for Advanced Study, Princeton, 1969-1970
    Assistant Professor, M.I.T., 1970-1973
    Associate Professor, M.I.T., 1973-1977
    Visiting Fellow, Imperial College, London, 1974
    Visiting Professor, Imperial College, London, 1986-1987
    Visiting Professor, Technion, Haifa, Israel, fall term, 1995
    Visiting Professor, Imperial College, London, 1995-1996
    Visiting Professor, Imperial College, London, 2003-2004
    Professor of Physics, Washington University, 1977 to present
    Scientific Consultant, Los Alamos National Laboratory, 1979-present
    Visiting Professor, Mathematics Department, Imperial College, London, 2006-2011
    Joint Professor of Physics, University of Heidelberg, 2008-2012
    Visiting Professor, King's College, London, 2011 to present
    International Professor of Physics, University of Heidelberg, 2012-present
    Visiting Professor, Department of Mathematical Sciences, City University London, 2013-2015


    Sloan Foundation Fellowship, 1972-1977
    Burlington Northern Foundation Faculty Achievement Award, 1985
    M.I.T. Graduate Student Council Teaching Award, 1976
    Washington University Gargoyle Award (Undergraduate Teaching Award) 1983
    Fulbright Fellowship to United Kingdom, 1995-1996
    Particle Physics and Astronomy Research Council (UK) Fellowship, 1996
    Lady Davis Fellowship to Israel, 1995-1996
    Rockefeller Foundation Award to Visit Bellagio Study and Conference Center, Italy, 1999
    Graduate Student Council Mentoring Award, 2000
    Fellows Award, Academy of Science of St. Louis, 2002
    Engineering and Physical Sciences Research Council (UK) Fellowship, 2003-2004
    John Simon Guggenheim Memorial Foundation Fellowship, 2003-2004
    Ulam Fellowship, Los Alamos National Laboratory, 2006-2007
    Compton Faculty Achievement Award, Washington University, 2007
    Wilfred R. and Ann Lee Konneker Distinguished Professor of Physics, 2007
    Leverhulme Foundation (UK) Fellowship, 2011-2012
    Associate Member, Higgs Centre, University of Edinburgh, 2012-present
    International Travel Grant, Royal Society, U.K. (with Prof. S. Sarkar), 2012-2014
    Dannie Heineman Prize for Mathematical Physics, 2017
    Humboldt Research Award, 2018

    Professional Societies

    American Physical Society (Elected a Fellow, 1978)
    Academy of Science of St. Louis (Elected a Fellow, 2002)
    Institute of Physics, UK (Elected a Fellow, 2004)



    Turbulence: Saturday Morning Seminar Series, 2008

    PT Symmetry in Quantum and Classical Physics

    PT Symmetry in Quantum and Classical Physics

    Originated by the author in 1998, the field of PT (parity-time) symmetry has become an extremely active and exciting area of research. PT-symmetric quantum and classical systems have theoretical, experimental, and commercial applications, and have been the subject of many journal articles, PhD theses, conferences, and symposia. Carl Bender's work has influenced major advances in physics and generations of students. This book is an accessible entry point to PT symmetry, ideal for students and scientists looking to begin their own research projects in this field.

    Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory

    Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory

    The main purpose of our book is to present and explain mathematical methods for obtaining approximate analytical solutions to differential and difference equations that cannot be solved exactly. Our objective is to help young and also established scientists and engineers to build the skills necessary to analyze equations that they encounter in their work. Our presentation is aimed at developing the insights and techniques that are most useful for attacking new problems. We do not emphasize special methods and tricks which work only for the classical transcendental functions; we do not dwell on equations whose exact solutions are known. The mathematical methods discussed in this book are known collectively as­ asymptotic and perturbative analysis. These are the most useful and powerful methods for finding approximate solutions to equations, but they are difficult to justify rigorously. Thus, we concentrate on the most fruitful aspect of applied analysis; namely, obtaining the answer. We stress care but not rigor. To explain our approach, we compare our goals with those of a freshman calculus course. A beginning calculus course is considered successful if the students have learned how to solve problems using calculus.