Quasiseparation of variables in the Schrödinger equation with a magnetic field

DOI10.1063/1.2399087zbMath1121.81064arXivmath-ph/0502046OpenAlexW1970422874MaRDI QIDQ3442155

C. Hudon, François Charest, Pavel Winternitz

Publication date: 16 May 2007

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

Full work available at URL: https://arxiv.org/abs/math-ph/0502046

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Groups and algebras in quantum theory and relations with integrable systems (81R12) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (11)

Family of nonstandard integrable and superintegrable classical Hamiltonian systems in non-vanishing magnetic fields ⋮ Three-dimensional superintegrable systems in a static electromagnetic field ⋮ Cylindrical type integrable classical systems in a magnetic field ⋮ Hydrogen atom in a magnetic field as an exactly solvable system without dynamical symmetries? ⋮ New classes of quadratically integrable systems in magnetic fields: the generalized cylindrical and spherical cases ⋮ Spherical type integrable classical systems in a magnetic field ⋮ Classical superintegrable systems in a magnetic field that separate in Cartesian coordinates ⋮ Superintegrable 3D systems in a magnetic field corresponding to Cartesian separation of variables ⋮ Generalized MICZ-Kepler system, duality, polynomial, and deformed oscillator algebras ⋮ Integrable generalisations of Dirac magnetic monopole ⋮ Superintegrability of separable systems with magnetic field: the cylindrical case

Cites Work

• Pure quantum integrability
• Integrable and superintegrable Hamiltonian systems in magnetic fields
• Superintegrable systems in quantum mechanics and classical Lie theory
• Variable separation for natural Hamiltonians with scalar and vector potentials on Riemannian manifolds
• Exact solvability of superintegrable systems
• Integrable Hamiltonian systems with vector potentials
• Integrable Hamiltonian systems with velocity-dependent potentials
• Group theory of the Smorodinsky–Winternitz system
• On superintegrable symmetry-breaking potentials in N-dimensional Euclidean space
• On separable Schrödinger equations
• Superintegrability in three-dimensional Euclidean space
• On separable Pauli equations
• Superintegrability with third-order integrals in quantum and classical mechanics
• Superintegrable systems in Darboux spaces
• Hamiltonians separable in Cartesian coordinates and third-order integrals of motion
• Integrable and superintegrable quantum systems in a magnetic field

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