Superintegrable systems from block separation of variables and unified derivation of their quadratic algebras

Abstract

We present a new method for constructing $D$-dimensional minimally superintegrable systems based on block coordinate separation of variables. We give two new families of superintegrable systems with $N$ ($N\le D$) singular terms of the partitioned coordinates and involving arbitrary functions. These Hamiltonians generalize the singular oscillator and Kepler systems. We derive their exact energy spectra via separation of variables. We also obtain the quadratic algebras satisfied by the integrals of motion of these models. We show how the quadratic symmetry algebras can be constructed by novel application of the gauge transformations from those of the non-partitioned cases. We demonstrate that these quadratic algebraic structures display an universal nature to the extent that their forms are independent of the functions in the singular potentials.

arXiv comment13 pages, no figure; Version to appear in Annals of Physics

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Cited by in corpus (6)

• Racah Algebra $R(n)$ from Coalgebraic Structures and Chains of $R(3)$ Substructures
• Polynomial algebras from $su(3)$ and the generic model on the two sphere
• New infinite families of $N$th-order superintegrable systems separating in Cartesian coordinates
• Hidden symmetry algebra and construction of quadratic algebras of superintegrable systems
• $N$-dimensional Smorodinsky-Winternitz model and related higher rank quadratic algebra $\mathcal{S}\mathcal{W}(N)$
• Polynomial algebras of superintegrable systems separating in Cartesian coordinates from higher order ladder operators