New exactly solvable systems with Fock symmetry

Abstract

New superintegrable systems are presented which, like the Hydrogen atom, possess a dynamical symmetry w.r.t. algebra o(4). One of them simulates a neutral fermion with non-trivial dipole moment, interacting with the external e.m. field. This system is presented in both non-relativistic and relativistic formulations. Another recently discovered system (see arXiv:1208.2886v1) is non-relativistic and includes the minimal and spin-orbit interaction with the external electric field. It is shown that all the considered systems are shape invariant. Applying this quality, these systems are integrated using the tools of SUSY quantum mechanics.

Section 6 and some new references are added

References in corpus (1)

• SU(2) Symmetry and Degeneracy From SUSY QM of a Neutron in the Magnetic Field of a Linear Current

Cited by in corpus (11)

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• Superintegrable and shape invariant systems with position dependent mass
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• Superintegrable systems with spin induced by coalgebra symmetry
• Superintegrable systems with spin invariant with respect to the rotation group
• Higher Order Quantum Superintegrability: a new "Painlevé conjecture"
• 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
• Integrable and superintegrable quantum mechanical systems with position dependent masses invariant with respect to one parametric Lie groups. 2. Systems with dilatation and shift symmetries