Biorthogonal quantum systems

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)(2)+Sigma(k > 0)mu(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. (c) 2007 American Institute of Physics.