Completeness and orthonormality in PT-symmetric quantum systems

Weigert, S. (2003) Completeness and orthonormality in PT-symmetric quantum systems. Physical Review A. art no. 062111. ISSN 1050-2947

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Abstract

Some PT-symmetric non-Hermitian Hamiltonians have only real eigenvalues. There is numerical evidence that the associated PT-invariant energy eigenstates satisfy an unconventional completeness relation. An ad hoc scalar product among the states is positive definite only if a recently introduced "charge operator" is included in its definition. A simple derivation of the conjectured completeness and orthonormality relations is given. It exploits the fact that PT symmetry provides a link between the eigenstates of the Hamiltonian and those of its adjoint, forming a dual pair of bases. The charge operator emerges naturally upon expressing the properties of the dual bases in terms of one basis only, and it is shown to be a function of the Hamiltonian.

Item Type:	Article
Copyright, Publisher and Additional Information:	© 2003 The American Physical Society. Reproduced in accordance with the publisher's self-archiving policy.
Academic Units:	The University of York > Mathematics (York)
Depositing User:	Repository Officer
Date Deposited:	23 Jun 2006
Last Modified:	19 Feb 2013 11:56
Published Version:	http://dx.doi.org/10.1103/PhysRevA.68.062111
Status:	Published
Refereed:	Yes
Related URLs:	http://www-users.york.ac.uk/~slow500/Pub... http://link.aps.org/abstract/PRA/v68/e06...
URI:	http://eprints.whiterose.ac.uk/id/eprint/1372

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