# PT-symmetric operators and metastable states of the 1D relativistic oscillators

@article{Giachetti2010PTsymmetricOA,
title={PT-symmetric operators and metastable states of the 1D relativistic oscillators},
author={Riccardo Giachetti and Vincenzo Grecchi},
journal={arXiv: Mathematical Physics},
year={2010}
}
• Published 20 May 2010
• Mathematics, Physics
• arXiv: Mathematical Physics
We consider the one-dimensional Dirac equation for the harmonic oscillator and the associated second order separated operators giving the resonances of the problem by complex dilation. The same operators have unique extensions as closed PT-symmetric operators defining infinite positive energy levels converging to the Schroedinger ones as c tends to infinity. Such energy levels and their eigenfunctions give directly a definite choice of metastable states of the problem. Precise numerical…
11 Citations

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