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

被引：2

作者：

Shapiro, Boris ^{[1
]}

Tater, Milos ^{[2
]}

机构：

[1] Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden

[2] Acad Sci, Nucl Phys Inst, Dept Theoret Phys, Rez Near Prague, Czech Republic

来源：

EXPERIMENTAL MATHEMATICS | 2019年 / 28卷 / 01期

关键词：

monodromy; spectral surface; spectrum of an harmonic oscillator;

D O I：

10.1080/10586458.2017.1325792

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：16 / 23

页数：8

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