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arXiv · 0707.1781

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

David Krejcirik
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Abstract

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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David Krejcirik. 2007-07-12. Calculation of the metric in the Hilbert space of a PT-symmetric model via the spectral theorem. https://doi.org/10.1088/1751-8113/41/24/244012

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