The relativistic rotated harmonic oscillator
A. Balmaseda, D. Krejcirik, J.M. P\'erez-Pardo
TL;DR
This paper develops a relativistic version of a non-self-adjoint harmonic oscillator, revealing complex pseudospectral properties and non-basis eigenfunctions despite a real, discrete spectrum.
Contribution
It introduces a relativistic extension of a non-self-adjoint harmonic oscillator and analyzes its spectral and pseudospectral characteristics.
Findings
Spectrum is real and discrete
Eigenfunctions do not form a basis
Pseudospectra are highly non-trivial
Abstract
We introduce a relativistic version of the non-self-adjoint operator obtained by a dilation analytic transformation of the quantum harmonic oscillator. While the spectrum is real and discrete, we show that the eigenfunctions do not form a basis and that the pseudospectra are highly non-trivial.
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Taxonomy
TopicsExperimental and Theoretical Physics Studies · Particle Accelerators and Free-Electron Lasers