Classical and Quantum Superintegrability of Stäckel Systems

  title={Classical and Quantum Superintegrability of St{\"a}ckel Systems},
  author={Maciej Błaszak and Krzysztof Marciniak},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  • M. BłaszakK. Marciniak
  • Published 16 August 2016
  • Mathematics
  • Symmetry Integrability and Geometry-methods and Applications
In this paper we discuss maximal superintegrability of both classical and quantum Stackel systems. We prove a sufficient condition for a flat or constant curvature Stackel system to be maximally su ... 

Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics

A non-degenerate second-order maximally conformally superintegrable system in dimension 2 naturally gives rise to a quadric with position dependent coefficients. It is shown how the system's Stackel

Non-Homogeneous Hydrodynamic Systems and Quasi-Stackel Hamiltonians

In this paper we present a novel construction of non-homogeneous hydrodynamic equations from what we call quasi-Stackel systems, that is non-commutatively integrable systems constructed from approp

Stäckel transform of Lax equations

We construct a map between Lax equations for pairs of Liouville integrable Hamiltonian systems related by a multiparameter Stäckel transform. Using this map, we construct Lax representation for a

Modified Laplace-Beltrami quantization of natural Hamiltonian systems with quadratic constants of motion

It is natural to investigate if the quantization of integrable or superintegrable classical Hamiltonian systems is still integrable or superintegrable. We study here this problem in the case of

Algebraic Conditions for Conformal Superintegrability in Arbitrary Dimension

Second-order conformally superintegrable systems generalise second-order (properly) superintegrable systems. They have been classified, essentially, in dimensions two and (partially) three only. For



Maximal superintegrability of Benenti systems

For a class of Hamiltonian systems, naturally arising in the modern theory of separation of variables, we establish their maximal superintegrability by explicitly constructing the additional

Exact solvability of superintegrable Benenti systems

We establish quantum and classical exact solvability for two large classes of maximally superintegrable Benenti systems in n dimensions with arbitrarily large n. Namely, we solve the Hamilton-Jacobi

Generalized Stäckel systems

Flat coordinates of flat Stäckel systems

A class of nonconservative Lagrangian systems on Riemannian manifolds

We generalize results of Rauch-Wojciechowski, Marciniak and Lundmark, concerning a class of nonconservative Lagrangian systems, from the Euclidean to the Riemannian case.

Second-order superintegrable systems in conformally flat spaces. V. Two- and three-dimensional 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

Natural coordinates for a class of Benenti systems

Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two-dimensional manifold

In this paper we prove that the two-dimensional superintegrable systems with quadratic integrals of motion on a manifold can be classified by using the Poisson algebra of the integrals of motion.

A maximally superintegrable deformation of the N-dimensional quantum Kepler–Coulomb system

The N-dimensional quantum Hamiltonian is shown to be exactly solvable for any real positive value of the parameter η. Algebraically, this Hamiltonian system can be regarded as a new maximally