Quasi-exactly solvable quartic: elementary integrals and asymptotics

Details Quasi-exactly solvable quartic: elementary integrals and asymptotics Quasi-exactly solvable quartic: elementary integrals and asymptotics

2011-04-12

arxiv.org/abs/1104.2305v2

J. Phys. A: Math. Theor. 44 (2011) 312001

Physics

Mathematical Physics

20 pages, 1 figure. Added Introduction and several references, corrected misprints

Scientific paper

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.

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