Toward classification of 2nd order superintegrable systems in 3-dimensional conformally flat spaces with functionally linearly dependent symmetry operators

DOI10.3842/SIGMA.2020.135zbMath1470.35022arXiv2004.00933MaRDI QIDQ2223053

Bjorn K. Berntson, Ernest G. Kalnins, Willard jun. Miller

Publication date: 28 January 2021

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.00933

zbMATH Keywords

superintegrable systemsCalogero 3 body systemfunctional linear dependence

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Groups and algebras in quantum theory and relations with integrable systems (81R12) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Geometric theory, characteristics, transformations in context of PDEs (35A30) Hamilton-Jacobi equations in mechanics (70H20) Symmetries, invariants, etc. in context of PDEs (35B06) Special quantum systems, such as solvable systems (81Q80)

Related Items (3)

Symmetries of Schrödinger–Pauli equations for charged particles and quasirelativistic Schrödinger equations ⋮ Superintegrable quantum mechanical systems with position dependent masses invariant with respect to two parametric Lie groups ⋮ Superintegrable and scale-invariant quantum systems with position-dependent Mass

Cites Work

• Three integrable Hamiltonian systems connected with isospectral deformations
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• Toward a classification of semidegenerate 3D superintegrable systems
• Nondegenerate 2D complex Euclidean superintegrable systems and algebraic varieties
• Second-order superintegrable systems in conformally flat spaces. I. Two-dimensional classical structure theory
• Second order superintegrable systems in conformally flat spaces. III. Three-dimensional classical structure theory
• Second-order superintegrable systems in conformally flat spaces. V. Two- and three-dimensional quantum systems
• A class of superintegrable systems of Calogero type
• Superintegrability of the Calogero–Moser system: Constants of motion, master symmetries, and time-dependent symmetries
• Separation of Variables and Superintegrability
• Erratum: Solution of the one-dimensional N-body problems with quadratic and/or inversely quadratic pair potentials [J. Math. Phys. 12, 419–436 (1971)]
• Fine structure for 3D second-order superintegrable systems: three-parameter potentials
• What an Effective Criterion of Separability says about the Calogero Type Systems

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