Superintegrable systems with spin and second-order tensor and pseudo-tensor integrals of motion


YURDUŞEN İ. , TUNCER O. O. , Winternitz P.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol.54, no.30, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 30
  • Publication Date: 2021
  • Doi Number: 10.1088/1751-8121/ac0a9e
  • Title of Journal : JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

Abstract

We investigate a quantum non-relativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. Assuming that the Hamiltonian is rotationally invariant and parity conserving we identify all such systems which allow additional tensor and pseudo-tensor integrals of motion that are second-order matrix polynomials in the momenta. Previously we found all the scalar, pseudo-scalar, vector and axial vector integrals of motion. No non-obvious tensor integrals exist. However, nontrivial pseudo-tensor integrals do exist. Together with our earlier results we give a complete list of such superintegrable Hamiltonian systems allowing second-order integrals of motion.