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Quantum two-dimensional superintegrable systems in flat space: exact-solvability, hidden algebra, polynomial algebra of integrals
Alexander V Turbiner, Juan Carlos Lopez Vieyra, Pavel Winternitz
In this short review paper the detailed analysis of six two-dimensional quantum {\it superintegrable} systems in flat space is presented. It includes the Smorodinsky-Winternitz pot…
On the spectral theory in the Fock space with polynomial eigenfunctions
A. V. Turbiner, N. L. Vasilevski
The notion of the eigenvalue problem in the Fock space with polynomial eigenfunctions is introduced. This problem is classified by using the finite-dimensional representations of t…
Tremblay-Turbiner-Winternitz (TTW) system at integer index : polynomial algebras of integrals
Juan Carlos López Vieyra, Alexander V Turbiner
An infinite 3-parametric family of superintegrable and exactly-solvable quantum models on a plane, admitting separation of variables in polar coordinates, marked by integer index $…
SUSY Quantum Mechanics, (non)-Analyticity and Phase Transitions
Alexander V Turbiner
It is shown by analyzing the Schrödinger equation that discontinuities in the coupling constant can occur in both the energies and the eigenfunctions. Surprisingly, those disc…