2012/05/31 by A. G. Nikitin · 1 citation
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Dipole #Geometry #Group (periodic table) #Hydrogen atom #Invariant (physics) #Mathematical physics #Mathematics #Physics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Quantum system #Symmetry (geometry) #Theoretical physics #math-ph #math.MP #msc:81Qxx #msc:81Vxx
paper · pdf · doi:10.1088/1751-8113/45/48/485204
published as J. Phys. A: Math. Theor. 45 (2012) 485204 (9pp) · Section 6 and some new references are added
openalex publication_date 2012/11/19 · arxiv created 2013/03/06 · arxiv updated 2015/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
New superintegrable systems are presented which, like the hydrogen atom, possess a dynamical symmetry w.r.t. algebra o(4). One system 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 Désilets et al 2012 arXiv:1208.2886v1) is non-relativistic and includes minimal and spin–orbit interaction with the external electric field. It is shown that all the systems considered are shape invariant. Applying this quality, these systems are integrated using the tools of SUSY quantum mechanics.