Carl M. Bender

Carl M. Bender ( born 1943 ) is an American physicist who is engaged in applied mathematics and mathematical physics.

Life

Bender studied physics at Cornell University ( Bachelor's degree summa cum laude 1964) and at Harvard University, where in 1965 he took his master's degree and received his doctorate in Sidney Coleman 1969. 1969/70 he was at the Institute for Advanced Study and then at the Massachusetts Institute of Technology, where he was an assistant professor in 1970 and associate professor in 1973. Since 1977 he is a professor at Washington University. He has been a visiting professor at Imperial College in London ( 1986/87, 1995/96, 2003/2004, since 2006), the Technion (1995) and consultant to the Los Alamos National Laboratory ( LANL, 1979 ). Since 2007 he is professor at the Ruprecht -Karls- University of Heidelberg.

Work

Bender dealt among other things with quantum field theory, perturbation theory of high order 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 the space dimension, dimensional expansions, finite element methods, Delta expansion). With Steven Orszag, he wrote a book on mathematics for scientists and engineers.

In 1998, he led a PT- symmetric quantum mechanics. PT stands for space and time reflection symmetry. It is a kind of continuation of quantum mechanics to the complex with non hermiteschem Hamiltonian ( Complex Quantum Mechanics by Bender), with Bender in 1998 showed that even then the spectrum could be real and positive, and he showed 2002 that a unitary time evolution can be constructed. Bender sees this as a more flexible formulation of quantum mechanics with ways to simplify calculation and new perspectives ( dark energy theories with difference in mass of particles and antiparticles, new interpretation of the spirit states in some models of quantum field theory). He also examined complexified systems of classical mechanics as the pendulum.

1972 to 1977 he was a Sloan Fellow, 2003-2004 Guggenheim Fellow, Fulbright Fellow in 1995 and he was also the 2006/2007 Ulam Fellow at LANL. He is a Fellow of the Institute of Physics and the American Physical Society.

Writings

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