Biorthogonal quantum systems

Journal Article · Sat Sep 15 00:00:00 EDT 2007 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2196243· OSTI ID:21013635

Curtright, Thomas; Mezincescu, Luca ^[1]

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1. Department of Physics, University of Miami, Coral Gables, Florida 33124 (United States) and School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540 (United States)

Models of PT symmetric quantum mechanics provide examples of biorthogonal quantum systems. The latter incorporate 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}){sup 2}+{sigma}{sub k>0}{mu}{sub k} exp(ikx). In some nontrivial cases, equivalent Hermitian theories are obtained and shown to be very simple: They are just free (chiral) particles. Field theory extensions are briefly considered.

• OSTI ID: 21013635
• Journal Information: Journal of Mathematical Physics, Vol. 48, Issue 9; Other Information: DOI: 10.1063/1.2196243; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CHIRALITY
GEOMETRY
QUANTUM FIELD THEORY
QUANTUM MECHANICS
SCHROEDINGER EQUATION