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Spectral properties of the massless relativistic quartic oscillator
journal contribution
posted on 2017-11-29, 15:52 authored by Samuel O. Durugo, Jozsef LorincziAn explicit solution of the spectral problem of the non-local Schrodinger operator obtained as the sum of the square root of the Laplacian and a quartic potential in
one dimension is presented. The eigenvalues are obtained as zeroes of special functions re-
lated to the fourth order Airy function, and closed formulae for the Fourier transform of the
eigenfunctions are derived. These representations allow to derive further spectral properties
such as estimates of spectral gaps, heat trace and the asymptotic distribution of eigenvalues, as well as a detailed analysis of the eigenfunctions. A subtle spectral effect is observed
which manifests in an exponentially tight approximation of the spectrum by the zeroes of
the dominating term in the Fourier representation of the eigenfunctions and its derivative.
History
School
- Science
Department
- Mathematical Sciences
Published in
Journal of Differential EquationsVolume
264Issue
5Pages
3775 - 3809Citation
DURUGO, S.O. and LORINCZI, J., 2018. Spectral properties of the massless relativistic quartic oscillator. Journal of Differential Equations, 264 (5), pp. 3775-3809.Publisher
© ElsevierVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Acceptance date
2017-11-27Publication date
2017-12-08Notes
This paper was accepted for publication in the journal Journal of Differential Equations and the definitive published version is available at https://doi.org/10.1016/j.jde.2017.11.030ISSN
0022-0396Publisher version
Language
- en