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