Superintegrable systems with spin invariant with respect to the rotation group

Abstract

Quantum nonrelativistic systems with $2\times2$ 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.