Conjectures that for integer k the TTW Hamiltonian H and integrals I1, I2, I12 generate a polynomial algebra of order k+1 inside hidden algebra g^(k), verified explicitly for k=1 to 4.
An infinite family of solvable and integrable quantum systems on a plane
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abstract
An infinite family of exactly-solvable and integrable potentials on a plane is introduced. It is shown that all already known rational potentials with the above properties allowing separation of variables in polar coordinates are particular cases of this family. The underlying algebraic structure of the new potentials is revealed as well as its hidden algebra. We conjecture that all members of the family are also superintegrable and demonstrate this for the first few cases. A quasi-exactly-solvable and integrable generalization of the family is found.
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math-ph 2years
2025 2verdicts
UNVERDICTED 2representative citing papers
Review confirms exact solvability, algebraic forms, hidden Lie algebras, and polynomial integral algebras for six 2D superintegrable systems including Smorodinsky-Winternitz, Fokas-Lagerstrom, Calogero-Wolfes, and TTW models.
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Tremblay-Turbiner-Winternitz (TTW) system at integer index $k$: polynomial algebras of integrals
Conjectures that for integer k the TTW Hamiltonian H and integrals I1, I2, I12 generate a polynomial algebra of order k+1 inside hidden algebra g^(k), verified explicitly for k=1 to 4.
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Quantum two-dimensional superintegrable systems in flat space: exact-solvability, hidden algebra, polynomial algebra of integrals
Review confirms exact solvability, algebraic forms, hidden Lie algebras, and polynomial integral algebras for six 2D superintegrable systems including Smorodinsky-Winternitz, Fokas-Lagerstrom, Calogero-Wolfes, and TTW models.