Biorthogonal Quantum Systems

Details Biorthogonal Quantum Systems Biorthogonal Quantum Systems

2005-07-04

arxiv.org/abs/quant-ph/0507015v3

J.Math.Phys.48:092106,2007

Physics

Quantum Physics

34 pages, 5 eps figures; references added and other changes made to conform to journal version

Scientific paper

10.1063/1.2196243

Models of PT symmetric quantum mechanics provide examples of biorthogonal quantum systems. The latter incorporporate all the structure of PT symmetric models, and allow for generalizations, especially in situations where the PT construction of the dual space fails. The formalism is illustrated by a few exact results for models of the form H=(p+\nu)^2+\sum_{k>0}\mu_{k}exp(ikx). In some non-trivial cases, equivalent hermitian theories are obtained and shown to be very simple: They are just free (chiral) particles. Field theory extensions are briefly considered.

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