Superintegrability in the interaction of two particles with spin

Tuncer O. O., Yurduşen İ.

JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL, cilt.58, ss.1-41, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 58
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1088/1751-8121/adde03
  • Dergi Adı: JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, INSPEC, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1-41
  • Hacettepe Üniversitesi Adresli: Evet

Özet

We initiate a research program for the systematic investigation of quantum superintegrable systems involving the interaction of two non-relativistic particles with spin 1/2 moving in the three-dimensional Euclidean space. In this paper, we focus specifically on such superintegrable systems that allow additional scalar integrals of motion, linear in the momenta. We first identify specific potentials appearing in the Hamiltonian that should be excluded from the analysis, as they can be immediately derived through gauge transformations of the natural Hamiltonian. Next, we construct the most general symmetric scalar operator and derive the determining equations from its commutation with the Hamiltonian. Solving these equations, we obtain 30 new superintegrable systems with spin, along with their corresponding first-order scalar integrals of motion.