The Gram Matrix of a PT-symmetric Quantum System

Details The Gram Matrix of a PT-symmetric Quantum System The Gram Matrix of a PT-symmetric Quantum System

2003-10-08

arxiv.org/abs/quant-ph/0310050v1

Czech. J. Phys. 54 (2004) 147

Physics

Quantum Physics

3 pages, no figures

Scientific paper

10.1023/B:CJOP.0000014380.30604.

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.

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