PT-symmetric Quantum Mechanics

Physics Colloquium 23rd May Delivered by Professor Carl M. Bender The average quantum physicist on the street would say that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to guarantee that the energy eigenvalues are real and that time evolution is unitary. However, the Hamiltonian $H=p^2+ix^3$, which is obviously not Dirac Hermitian, has a positive real discrete spectrum and generates unitary time evolution, and thus it defines a fully consistent and physical quantum theory! Evidently, the axiom of Dirac Hermiticity is too restrictive. While $H=p^2+ix^3$ is not Dirac Hermitian, it is PT symmetric; that is, invariant under combined parity P (space reflection) and time reversal T. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics is extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past four years, some of these properties have been verified in many laboratory experiments. A particularly interesting PT-symmetric Hamiltonian is $H=p^2-x^4$, which contains an upside-down potential. We will discuss this potential in detail, and explain in intuitive as well as in rigorous terms why the energy levels of this potential are real, positive, and discrete. Creative Commons Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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The Department of Physics public lecture series. An exciting series of lectures about the research at Oxford Physics take place throughout the academic year. Looking at topics diverse as the creation of the universe to the science of climate change. Features episodes previously published as: (1) 'Oxford Physics Alumni': "Informal interviews with physics alumni at events, lectures and other alumni related activities." (2) 'Physics and Philosophy: Arguments, Experiments and a Few Things in Between': "A series which explores some of the links between physics and philosophy, two of the most fundamental ways with which we try to answer our questions about the world around us. A number of the most pertinent topics which bridge the disciplines are discussed - the nature of space and time, the unpredictable results of quantum mechanics and their surprising consequences and perhaps most fundamentally, the nature of the mind and how far science can go towards explaining and understanding it. Featuring interviews with Dr. Christopher Palmer, Prof. Frank Arntzenius, Prof. Vlatko Vedral, Dr. David Wallace and Prof. Roger Penrose."