Quasi-exactly solvable quartic: elementary integrals and asymptotics
Mathematical Physics
2015-05-27 v2 Classical Analysis and ODEs
math.MP
Abstract
We study elementary eigenfunctions y=p exp(h) of operators L(y)=y"+Py, where p, h and P are polynomials in one variable. For the case when h is an odd cubic polynomial, we found an interesting identity which is used to describe the spectral locus. We also establish some asymptotic properties of the QES spectral locus.
Cite
@article{arxiv.1104.2305,
title = {Quasi-exactly solvable quartic: elementary integrals and asymptotics},
author = {Alexandre Eremenko and Andrei Gabrielov},
journal= {arXiv preprint arXiv:1104.2305},
year = {2015}
}
Comments
20 pages, 1 figure. Added Introduction and several references, corrected misprints