Carl Bender

Konneker Distinguished Professor of Physics Emeritus
PhD, Harvard University
AM, Harvard University
AB, Cornell University
research interests:
  • Theoretical & Mathematical Physics
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contact info:

mailing address:

  • CB 1105
  • 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.