Superintegrable systems with spin invariant with respect to the rotation group

Abstract

Quantum nonrelativistic systems with $2\times 2$ matrix potentials are investigated. Physically, they simulate charged or neutral fermions with non-trivial dipole momenta, interacting with an external electric field. Assuming rotationally invariance of the Hamiltonian all such systems allowing second order integrals of motion are identified. It is shown that the integrals of motion can be effectively used to separate variables and to reduce the systems to decoupled ordinary differential equations. Solutions for two of the discussed problems are presented explicitly.

24 pages, some misprints were corrected

References in corpus (7)

• Integrable and superintegrable systems with spin
• Quantum Super-Integrable Systems as Exactly Solvable Models
• New exactly solvable systems with Fock symmetry
• Quantum superintegrable system for arbitrary spin
• Superintegrable systems with spin invariant with respect to the rotation group
• Remarks on Multi-Dimensional Conformal Mechanics
• Generalized Killing Tensors and Symmetry of Klein-Gordon-Fock Equations

Cited by in corpus (9)

• Superintegrable systems with position dependent mass
• Superintegrable systems with spin induced by coalgebra symmetry
• Laplace-Runge-Lenz vector for arbitrary spin
• Superintegrable systems with spin invariant with respect to the rotation group
• Symmetries of Schroedinger equation with scalar and vector potentials
• Superintegrable systems with spin and second-order (pseudo)tensor integrals of motion
• Symmetries of the Schroedinger-Pauli equations for charged particles and quasirelativistic Schroedinger equations
• Symmetries of the Schroedinger-Pauli equation for neutral particles
• Superintegrability in the interaction of two particles with spin