The Gram Matrix of a PT-Symmetric Quantum System |
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| Authors: | Stefan Weigert |
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| Institution: | (1) Hull Mathematical Physics, Department of Mathematics, University of Hull, Hull, HU6 7RX, UK |
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| 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. |
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| Keywords: | Gram Matrix PT symmetry bi-orthonormal basis |
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