The Smorodinsky-Winternitz potential revisited
Roman G. Smirnov, Amelia L. Yzaguirre
TL;DR
This paper uses geometric invariants of Killing tensors to analyze the Smorodinsky-Winternitz potential, clarifying its parameters and exploring conditions for multi-separability of related potentials.
Contribution
It introduces a geometric approach to characterize the potential and determines parameter values for multi-separability, advancing understanding of superintegrable systems.
Findings
Characterization of the potential using joint invariants of Killing tensors
Identification of parameter values for multi-separability
Geometric interpretation of arbitrary parameters
Abstract
We employ joint invariants of Killing two-tensors defined in the Euclidean plane to characterize the Smorodinsky-Winternitz potential and explain the geometric meaning of its arbitrary parameters. In addition, we verify for which values of the arbitrary parameter the Tremblay-Turbiner-Winternitz potential is multi-separable.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Quantum chaos and dynamical systems · Nonlinear Waves and Solitons