Quantum integrable systems in three-dimensional magnetic fields: the Cartesian case

Abstract

In this paper we construct integrable three-dimensional quantum-mechanical systems with magnetic fields, admitting pairs of commuting second-order integrals of motion. The case of Cartesian coordinates is considered. Most of the systems obtained are new and not related to the separation of variables in the corresponding Schrödinger equation.

8 pages

References in corpus (2)

• Integrable and superintegrable quantum systems in a magnetic field
• Quasiseparation of variables in the Schroedinger equation with a magnetic field

Cited by in corpus (8)

• Three-dimensional superintegrable systems in a static electromagnetic field
• An Infinite Family of Maximally Superintegrable Systems in a Magnetic Field with Higher Order Integrals
• Cylindrical type integrable classical systems in a magnetic field
• On superintegrability of 3D axially-symmetric non-subgroup-type systems with magnetic fields
• On rotationally invariant integrable and superintegrable classical systems in magnetic fields with non-subgroup type integrals
• New classes of quadratically integrable systems in magnetic fields: the generalized cylindrical and spherical cases
• Hydrogen Atom in Electric and Magnetic Fields: Dynamical Symmetries, Superintegrable and Integrable Systems, Exact Solutions
• Cylindrical first order superintegrability with complex magnetic fields