Asymptotics and Monodromy of the Algebraic Spectrum of Quasi-Exactly Solvable Sextic Oscillator

0504324 - ÚJF 2020 RIV US eng J - Journal Article
Shapiro, B. - Tater, Miloš
Asymptotics and Monodromy of the Algebraic Spectrum of Quasi-Exactly Solvable Sextic Oscillator.
Experimental Mathematics. Roč. 28, č. 1 (2019), s. 16-23. ISSN 1058-6458. E-ISSN 1944-950X
R&D Projects: GA ČR(CZ) GA14-06818S
Institutional support: RVO:61389005
Keywords : monodromy * spectral surface * spectrum of an harmonic oscillator
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 0.659, year: 2019
Method of publishing: Limited access
https://doi.org/10.1080/10586458.2017.1325792

In this article we study numerically and theoretically the asymptotics of the algebraic part of the spectrum for the quasi-exactly solvable sextic potential pi(m, b)(x) = x(6) + 2bx(4) + (b(2) - (4m + 3))x(2), its level crossing points, and its monodromy in the complex plane of parameter b. Here m is a fixed positive integer. We also discuss the connection between the special sequence of quasi-exactly solvable sextics with increasing m and the classical quartic potential.
Permanent Link: http://hdl.handle.net/11104/0295986