Integrable and superintegrable quantum systems in a magnetic field

Details Integrable and superintegrable quantum systems in a magnetic field Integrable and superintegrable quantum systems in a magnetic field

2003-11-26

arxiv.org/abs/math-ph/0311051v1

J.Math.Phys. 45(5), 1959-1973 (2004)

Physics

Mathematical Physics

23 pages ,1 figure

Scientific paper

10.1063/1.1695447

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.

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