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Publications Influence

Advanced Mathematical Methods For Scientists And Engineers

- C. Bender, S. A. Orszag
- Mathematics
- 1978

This book gives a self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference… Expand

3,285 153

Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry

- C. Bender, S. Boettcher
- Physics, Mathematics
- 29 November 1997

The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of $\mathrm{PT}$ symmetry, one obtains new… Expand

3,287 126- PDF

Advanced mathematical methods for scientists and engineers I: asymptotic methods and perturbation theory.

- C. Bender, S. A. Orszag
- Physics
- 1999

933 71

Making sense of non-Hermitian Hamiltonians

- C. Bender
- Physics
- 9 March 2007

The Hamiltonian H specifies the energy levels and time evolution of a quantum theory. A standard axiom of quantum mechanics requires that H be Hermitian because Hermiticity guarantees that the energy… Expand

1,647 69- PDF

Complex extension of quantum mechanics.

Requiring that a Hamiltonian be Hermitian is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but satisfies the less… Expand

1,034 20- PDF

Introduction to 𝒫𝒯-symmetric quantum theory

- C. Bender
- Mathematics, Physics
- 11 January 2005

In most introductory courses on quantum mechanics one is taught that the Hamiltonian operator must be Hermitian in order that the energy levels be real and that the theory be unitary (probability… Expand

301 14- PDF

Quantum mechanical Carnot engine

- C. Bender, D. Brody, Bernhard K. Meister
- Physics
- 23 June 2000

A cyclic thermodynamic heat engine runs most efficiently if it is reversible. Carnot constructed such a reversible heat engine by combining adiabatic and isothermal processes for a system containing… Expand

155 13- PDF

A new perturbative approach to nonlinear problems

- C. Bender, K. A. Milton, S. Pinsky, L. Simmons
- Physics
- 1 July 1989

A recently proposed perturbative technique for quantum field theory consists of replacing nonlinear terms in the Lagrangian such as φ4 by (φ2)1+δ and then treating δ as a small parameter. It is shown… Expand

268 10

Parity–time-symmetric whispering-gallery microcavities

- B. Peng, S. Ozdemir, +7 authors L. Yang
- Physics, Mathematics
- 21 August 2013

It is now shown that coupled optical microcavities bear all the hallmarks of parity–time symmetry; that is, the system’s dynamics are unchanged by both time-reversal and mirror transformations. The… Expand

1,129 9- PDF