Superintegrable 3D systems in a magnetic field corresponding to Cartesian separation of variables

DOI10.1088/1751-8121/aa6f68zbMath1369.81050OpenAlexW2607755778MaRDI QIDQ4977135

Antonella Marchesiello, Libor Šnobl

Publication date: 3 August 2017

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1751-8121/aa6f68

zbMATH Keywords

integrabilitymagnetic fieldsuperintegrabilityclassical and quantum mechanics

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) 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)

Related Items (15)

Family of nonstandard integrable and superintegrable classical Hamiltonian systems in non-vanishing magnetic fields ⋮ Pairs of commuting quadratic elements in the universal enveloping algebra of Euclidean algebra and integrals of motion* ⋮ On rotationally invariant integrable and superintegrable classical systems in magnetic fields with non-subgroup type integrals ⋮ Cylindrical type integrable classical systems in a magnetic field ⋮ Hydrogen atom in a magnetic field as an exactly solvable system without dynamical symmetries? ⋮ Linearity of minimally superintegrable systems in a static electromagnetic field ⋮ Cylindrical first-order superintegrability with complex magnetic fields ⋮ New classes of quadratically integrable systems in magnetic fields: the generalized cylindrical and spherical cases ⋮ Spherical type integrable classical systems in a magnetic field ⋮ An infinite family of maximally superintegrable systems in a magnetic field with higher order integrals ⋮ Superintegrability and time-dependent integrals ⋮ Higher Order Quantum Superintegrability: A New “Painlevé Conjecture” ⋮ Classical superintegrable systems in a magnetic field that separate in Cartesian coordinates ⋮ On superintegrability of 3D axially-symmetric non-subgroup-type systems with magnetic fields ⋮ Superintegrability of separable systems with magnetic field: the cylindrical case

Cites Work

• On integrable Hamiltonians with velocity-dependent potentials
• Pure quantum integrability
• Integrable and superintegrable Hamiltonian systems in magnetic fields
• Classical and quantum superintegrability with applications
• Integrable Hamiltonian systems with vector potentials
• Symmetries and degeneracies of a charged oscillator in the field of a magnetic monopole
• Quasiseparation of variables in the Schrödinger equation with a magnetic field
• Three-dimensional superintegrable systems in a static electromagnetic field
• Integrable Hamiltonian systems with velocity-dependent potentials
• Group theory of the Smorodinsky–Winternitz system
• Integrable and superintegrable quantum systems in a magnetic field
• SUSY approach to Pauli Hamiltonians with an axial symmetry

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