Weigert, S. orcid.org/0000-0002-6647-3252 (2003) Completeness and orthonormality in PT-symmetric quantum systems. Physical Review A. art no. 062111. ISSN 1094-1622
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.
|Copyright, Publisher and Additional Information:||© 2003 The American Physical Society. Reproduced in accordance with the publisher's self-archiving policy.|
|Institution:||The University of York|
|Academic Units:||The University of York > Mathematics (York)|
|Depositing User:||Repository Officer|
|Date Deposited:||23 Jun 2006|
|Last Modified:||03 Jan 2017 03:25|