Carl Bender, Department of Physics, Washington University

Friday March 23rd, 4pm, Phillips 332 (refreshments served in Phillips 330 starting at 3:30)

Making sense of non-Hermitian Hamiltonians

Abstract: It is a common belief that the Hamiltonian H in quantum mechanics must be Hermitian (in the Dirac sense) in order that the energy spectrum be real and that time evolution be unitary (probability conserving). In this talk we examine an alternative formulation of quantum mechanics in which the conventional requirement of Hermiticity is replaced by the more general and physical condition of space-time reflection (PT) symmetry. We show that even if a PT-symmetric Hamiltonian is non-Hermitian, its spectrum is real and positive and time evolution is unitary. Two amazing examples of such PT-symmetric non-Hermitian Hamiltonians are and . In effect, we are extending quantum mechanics into the complex domain. We will explain the physically observable differences between Hermitian Hamiltonians and non-Hermitian PT-symmetric Hamiltonians.