Intertwining Symmetry Algebras of Quantum Superintegrable Systems

Abstract

We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like $(su(n),so(2n))$ or $(su(p,q),so(2p,2q))$. The eigenstates of the associated Hamiltonian hierarchies belong to unitary representations of these algebras. It is shown that these intertwining operators, related with separable coordinates for the system, are very useful to determine eigenvalues and eigenfunctions of the Hamiltonians in the hierarchy. An study of the corresponding superintegrable classical systems is also included for the sake of completness.

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Cited by in corpus (5)

• Polynomial algebras from $su(3)$ and the generic model on the two sphere
• Superintegrable systems from block separation of variables and unified derivation of their quadratic algebras
• Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions
• Solution of Second Order Supersymmetrical Intertwining Relations in Minkowski Plane
• Non-Hermitian superintegrable systems