New exactly solvable systems with Fock symmetry

TL;DR

This paper introduces new exactly solvable superintegrable quantum systems with Fock symmetry, including models for neutral fermions and electric field interactions, all exhibiting shape invariance and solvable via SUSY quantum mechanics.

Contribution

It presents novel superintegrable systems with Fock symmetry, demonstrating their shape invariance and solvability through SUSY quantum mechanics, extending known models like the Hydrogen atom.

Findings

Systems possess o(4) dynamical symmetry.

All systems are shape invariant and integrable.

Models include neutral fermions and electric field interactions.

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.