Integrable and superintegrable quantum systems in a magnetic field
arXiv:math-ph/0311051 · doi:10.1063/1.1695447
Abstract
Integrable quantum mechanical systems with magnetic fields are constructed in two-dimensional Euclidean space. The integral of motion is assumed to be a first or second order Hermitian operator. Contrary to the case of purely scalar potentials, quadratic integrability does not imply separation of variables in the Schroedinger equation. Moreover, quantum and classical integrable systems do not necessarily coincide: the Hamiltonian can depend on the Planck constant in a nontrivial manner.
23 pages ,1 figure
References in corpus (7)
- Completeness of superintegrability in two-dimensional constant curvature spaces
- Superintegrability with third order invariants in quantum and classical mechanics
- Exact Solvability of Superintegrable Systems
- Superintegrable Systems in Darboux spaces
- Hamiltonians separable in cartesian coordinates and third-order integrals of motion
- Quantum superintegrability and exact solvability in N dimensions
- Pure quantum integrability
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