Calculation of the metric in the Hilbert space of a PT-symmetric model via the spectral theorem

Details Calculation of the metric in the Hilbert space of a PT-symmetric model via the spectral theorem Calculation of the metric in the Hilbert space of a PT-symmetric model via the spectral theorem

2007-07-12

arxiv.org/abs/0707.1781v1

J. Phys. A: Math. Theor. 41 (2008) 244012.

Physics

Mathematical Physics

LaTeX, 6 pages

Scientific paper

10.1088/1751-8113/41/24/244012

In a previous paper (arXiv:math-ph/0604055) we introduced a very simple PT-symmetric non-Hermitian Hamiltonian with real spectrum and derived a closed formula for the metric operator relating the problem to a Hermitian one. In this note we propose an alternative formula for the metric operator, which we believe is more elegant and whose construction -- based on a backward use of the spectral theorem for self-adjoint operators -- provides new insights into the nature of the model.

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