Asymptotics and Monodromy of the Algebraic Spectrum of Quasi-Exactly Solvable Sextic Oscillator. Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Shapiro, Boris; Tater, Miloš
• Is Part Of: Experimental mathematics. Volume 28:Issue 1(2019)
• Page Start: 16
• Page End: 23
• Publication Date: 2019-01-02
• Subjects: monodromy -- spectral surface -- spectrum of an harmonic oscillator; 81Q10; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: 10.1080/10586458.2017.1325792
• Languages: English
• ISSNs: 1058-6458

Abstract

ABSTRACT: In this article we study numerically and theoretically the asymptotics of the algebraic part of the spectrum for the quasi-exactly solvable sextic potential Π m, b ( x ) = x 6 + 2 bx 4 + ( b 2 − (4 m + 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.