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Quantum Simulation

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

arXiv

Authors: David Krejcirik

Year

2007

Paper ID

49693

Status

Preprint

Abstract Read

~2 min

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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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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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:0707.1781 [2] arXiv https://arxiv.org/abs/0707.1781 [3] Publisher https://arxiv.org/abs/0707.1781

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