The Harmonic Lagrange Top and the Confluent Heun Equation

被引：1
|
作者：
Dawson, Sean R. [1 ]
Dullin, Holger R. [1 ]
H. Nguyen, Diana M. [1 ]
机构：
[1] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia
来源：
REGULAR & CHAOTIC DYNAMICS | 2022年 / 27卷 / 04期
关键词：
symmetric rigid body; Lagrange top; Hamiltonian Hopf bifurcation; quantisation; confluent Heun equation; ROTATING BLACK-HOLE; RIGID-BODY; MONODROMY; PERTURBATIONS; SINGULARITIES; MOLECULE; SYSTEMS; MOTION;
D O I：
10.1134/S1560354722040049
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The harmonic Lagrange top is the Lagrange top plus a quadratic (harmonic) potential term. We describe the top in the space fixed frame using a global description with a Poisson structure on T *S-3. This global description naturally leads to a rational parametrisation of the set of critical values of the energy-momentum map. We show that there are 4 different topological types for generic parameter values. The quantum mechanics of the harmonic Lagrange top is described by the most general confluent Heun equation (also known as the generalised spheroidal wave equation). We derive formulas for an infinite pentadiagonal symmetric matrix representing the Hamiltonian from which the spectrum is computed.
引用
收藏
页码：443 / 459
页数：17
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