Liu Bie Ju Centre for Mathematical Sciences
City University of Hong Kong
Mathematical Analysis and its Applications
Colloquium

Organized by Prof. Philippe G. Ciarlet and Prof. Roderick Wong

Making Sense of Non-Hermitian Hamiltonians

by
Professor Carl M. Bender
Physics Department, Washington University in St. Louis
and
Center for Nonlinear Studies, Los Alamos National Laboratory

Date: November 22, 2006 (Wednesday)
Time: 4:30 pm to 5:30 pm
Venue: Room B6605 (Faculty Conference Room)
Blue Zone, Level 6
Academic Building
City University of Hong Kong

Abstract: It is a common belief that the Hamiltonian H must be Hermitian in order that the energy spectrum be real and that time evolution be unitary. 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 the time evolution is unitary. Two amazing examples of such PT-symmetric non-Hermitian Hamiltonians are H=p²+ix³ and H=p²-x⁴. In effect, we are extending quantum mechanics into the complex domain.

             

** All interested are welcome **

For enquiry: 2788-9816

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