The Gram Matrix of a PT-symmetric Quantum System
arXiv:quant-ph/0310050 · doi:10.1023/B:CJOP.0000014380.30604.a8
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.
3 pages, no figures