Parasupersymmetries and Non-Lie Constants of Motion for Two-Particle Equations

Abstract

We search for hidden symmetries of two-particle equations with oscillator-equivalent potential, proposed by Moshinsky with collaborators. We proved that these equations admit hidden symmetries and parasupersymmetries which enable one to easily find the Hamiltonian spectra using algebraic methods and to construct exact Foldy–Wouthuysen transformations. Moreover, we demonstrate that these equations are reducible and generate Hamiltonians for pararelativistic or Kemmer oscillators. We also establish equivalence relations between different approaches to Kemmer oscillator and propose new one- and two-particle equations with oscillator-equivalent potentials.