The Gram Matrix of a PT-symmetric Quantum System
Quantum Physics
2009-11-10 v1
Abstract
The eigenstates of a diagonalizable PT-symmetric Hamiltonian satisfy unconventional completeness and orthonormality relations. These relations reflect the properties of a pair of bi-orthonormal bases associated with non-hermitean diagonalizable operators. In a similar vein, such a dual pair of bases is shown to possess, in the presence of PT symmetry, a Gram matrix of a particular structure: its inverse is obtained by simply swapping the signs of some its matrix elements.
Keywords
Cite
@article{arxiv.quant-ph/0310050,
title = {The Gram Matrix of a PT-symmetric Quantum System},
author = {Stefan Weigert},
journal= {arXiv preprint arXiv:quant-ph/0310050},
year = {2009}
}
Comments
3 pages, no figures