Carl M. Bender

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Carl M. Bender (* 1943 ) is an American physicist who deals with applied mathematics and mathematical physics.

Life

Bender studied physics at Cornell University (bachelor's degree summa cum laude 1964) and at Harvard University , where he made his master's degree in 1965 and received his doctorate in 1969 with Sidney Coleman . In 1969/70 he was at the Institute for Advanced Study and then at the Massachusetts Institute of Technology , where he became an Assistant Professor in 1970 and an Associate Professor in 1973. Since 1977 he has been a professor at Washington University . Among other things, he was visiting professor at Imperial College in London (1986/87, 1995/96, 2003/2004, from 2006), at Technion (1995) and advisor to Los Alamos National Laboratory (LANL, from 1979). Since 2007 he has been a professor at the Ruprecht-Karls-Universität Heidelberg .

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Bender dealt with, among other things, quantum field theory , high-order perturbation theory in the anharmonic oscillator (with Tai Tsun Wu ,) and semi-classical methods, development of new perturbative methods in quantum mechanics and quantum field theory (such as development in spatial dimensions, dimensional expansions , finite element methods , Delta expansion ). With Steven Orszag he wrote a book on mathematics for scientists and engineers.

In 1998 he introduced PT-symmetric quantum mechanics. PT stands for space and time mirroring symmetry. It is a kind of continuation of quantum mechanics into the complex with a non-Hermitian Hamilton operator ( complex quantum mechanics according to Bender), whereby Bender showed in 1998 that the spectrum could then also be real and positive and he also showed in 2002 that a unitary time evolution can be constructed . Bender sees this as a more flexible formulation of quantum mechanics with possibilities for easier calculation and new perspectives (dark energy, theories with the difference in the mass of particles and antiparticles, new interpretation of the states of mind in some models of quantum field theory). He also examined complexified systems of classical mechanics such as the pendulum.

From 1972 to 1977 he was a Sloan Research Fellow , 2003 to 2004 Guggenheim Fellow, 1995 Fulbright Fellow and 2006/2007 Ulam Fellow at the LANL. He is a Fellow of the Institute of Physics and the American Physical Society , which awarded him their 2017 Dannie Heineman Prize for Mathematical Physics .

Fonts

  • with Steven Orszag: Advanced Mathematical Methods for Scientists and Engineers . Volume 1 (Asymptotic methods and perturbation theory). Springer 1999 (the forerunner edition in one volume was published by McGraw Hill in 1978)

Web links

Individual evidence

  1. ↑ Bender, Wu: The anharmonic oscillator , part 1,2. In: Physical Review , Volume 184, 1969, p. 1231, Physical Review D, Volume 7, 1973, p. 1620. Bender and Wu used a wide variety of mathematical methods. Her work became the starting point for later developments such as the investigation of instantons and the theory of hyperasymptotes.
  2. ^ Bender, Boettcher: Real Spectra in non hermitean hamiltonians having PT-Symmetry . In: Physical Review Letters , Volume 80, 1998, p. 5243. Bender, Brody, Jones: Complex extension of quantum mechanics . In: Physical Review Letters , Volume 89, 2002, pp. 270401. Bender, Brody, Jones: Must a Hamiltonian be Hermitian? In: American Journal of Physics , Volume 71, 2003, p. 1095, arxiv : hep-th / 0303005 . Bender: Making sense of non hermitean Hamiltonians . In: Rep. Progr. Phys. , 2007, arxiv : hep-th / 0703096 . Bender: Introduction to PT symmetric quantum theory . In: Contemporary Physics , 2005, arxiv : quant-ph / 0501052
  3. ^ Conditions of negative norm
  4. ^ Bender, Holm, Hook: Complexified dynamical systems . In: J. Phys. A , 2007, arxiv : 0705.3893 .
personal data
SURNAME Bender, Carl M.
BRIEF DESCRIPTION American physicist
DATE OF BIRTH 1943