Integrability and separation of variables in Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems

2015/09/30 by Tigran Hakobyan, Armen Nersessian
Chemistry · Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Center (category theory) #Chemistry #Coulomb #Degeneracy (biology) #Electric field #Electric potential energy #Elliptic coordinate system #Energy (signal processing) #Generalized coordinates #Integrable system #Log-polar coordinates #Mathematical physics #Nonlinear Waves and Solitons #Parabolic coordinates #Physics #Quantum mechanics #Spherical coordinate system #Stark effect #cond-mat.str-el #hep-th #math-ph #math.MP #nlin.SI #quant-ph

paper · pdf · doi:10.1103/physrevd.93.045025

published as Phys. Rev. D 93, 045025 (2016) · 18 pages

openalex publication_date 2016/02/23 · arxiv created 2016/02/25 · arxiv updated 2016/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We propose the integrable N-dimensional Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems and construct their constants of motion via the Dunkl operators. Their Schr"odinger equations decouple in parabolic and elliptic coordinates into the set of three differential equations like for the Coulomb-Stark and two-center Coulomb problems. The Calogero term preserves the energy levels, but changes their degrees of degeneracy.

Citations

• Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials
• Generalization of the Runge-Lenz Vector in the Presence of an Electric Field
• Action-angle variables for dihedral systems on the circle
• Hidden symmetries of integrable conformal mechanical systems
• Differential-difference operators associated to reflection groups
• Hidden symmetry of the quantum Calogero-Moser system