Abstract
In this paper, we investigate new integrable extensions of two-center Coulomb systems. We study the most general -dimensional deformation of the two-center problem by adding arbitrary functions supporting second-order commuting conserved quantities. The system is superintegrable for and, for certain choices of the arbitrary functions, reduces to known models previously discovered. Then, based on this extended system, we introduce an additional integrable generalization involving Calogero interactions for . In all examples, including the two-center problem, we explicitly present the complete list of Liouville integrals in terms of second-order integrals of motion.
- Received 25 January 2024
- Accepted 16 March 2024
DOI:https://doi.org/10.1103/PhysRevD.109.085011
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Published by the American Physical Society