• Corpus ID: 214774826

Classification of Calogero-like 2nd order superintegrable systems in 3 dimensions

  title={Classification of Calogero-like 2nd order superintegrable systems in 3 dimensions},
  author={Bjorn K Berntson and Ernie G. Kalnins and Willard Miller and Jr.},
  journal={arXiv: Mathematical Physics},
All 2nd order classical and quantum superintegrable systems in 3 dimensional conformally flat spaces with nondegenerate (i.e., 4-parameter) potentials have been classified and great progress has been made on the classification of semidegenerate (i.e., 3-parameter) potentials. By definition these admit 5 functionally linearly independent symmetry operators, i.e., they are not only linearly independent in the usual sense but also if the coefficients are allowed to depend on the spatial variables… 
A new way to classify 2D higher order quantum superintegrable systems
We revise a method by Kalnins, Kress and Miller (2010) for constructing a canonical form for symmetry operators of arbitrary order for the Schrodinger eigenvalue equation $H\Psi \equiv (\Delta_2


Toward a classification of semidegenerate 3D superintegrable systems
Superintegrable systems of 2nd order in 3 dimensions with exactly 3-parameter potentials are intriguing objects. Next to the nondegenerate 4-parameter potential systems they admit the maximum number
Second order superintegrable systems in conformally flat spaces . V : 2 D and 3 D quantum systems
This paper is the conclusion of a series that lays the groundwork for a structure and classification theory of second order superintegrable systems, both classical and quantum, in conformally flat
Fine structure for 3 D second order superintegrable systems : 3-parameter potentials
A classical (or quantum) superintegrable system of second order is an integrable n-dimensional Hamiltonian system with potential that admits 2n − 1 functionally independent constants of the motion
Nondegenerate 2D complex Euclidean superintegrable systems and algebraic varieties
A classical (or quantum) superintegrable system is an integrable n-dimensional Hamiltonian system with potential that admits 2n − 1 functionally independent constants of the motion polynomial in the
Invariant classification of second-order conformally flat superintegrable systems
In this paper we continue the work of Kalnins et al in classifying all second-order conformally-superintegrable (Laplace-type) systems over conformally flat spaces, using tools from algebraic
A class of superintegrable systems of Calogero type
We show that the three body Calogero model with inverse square potentials can be interpreted as a maximally superintegrable and multiseparable system in Euclidean three-space. As such it is a special
Superintegrability of the Calogero–Moser system: Constants of motion, master symmetries, and time-dependent symmetries
The classical n-dimensional Calogero–Moser system is a maximally superintegrable system endowed with a rich variety of symmetries and constants of motion. In the first part of the article some
What an Effective Criterion of Separability says about the Calogero Type Systems
Abstract In [15] we have proved a 1-1 correspondence between all separable coordinates on R n (according to Kalnins and Miller [9]) and systems of linear PDEs for separable potentials V (q). These
Superintegrability of the Calogero-Moser system☆
The super-separability of the three-body inverse-square Calogero system
The geometrical theory of the variable separation for the Hamilton–Jacobi equation is applied to the classical three-body inverse-square Calogero system. It is proved that this system is separable in