In the present paper I will briefly summarize some recent results about the solvability of the classical and quantum version of a (hyper-)spherically symmetric N-dimensional system living on a curved manifold characterized by a conformally flat metric. The system appears as a generalization of the so-called Taub–NUT system. We call it Quasi-Maximally Superintegrable (QMS) since it is endowed with 2N − 2 constants of the motion (with 2N − 1 it would have been Maximally Superintegrable (MS)) functionally independent and Poisson commuting in the Classical case, algebraically independent and commuting as operators in the Quantum case. The eigenvalues and eigenfunctions of the quantum system are explicitly given, while for the classical version we provide the analytic solution of the radial equation of motion. A few comments about the connection between exact solvability and superintegrability are made in the final part of the paper.
Ragnisco, O. (2021). A Confined Quasi-Maximally Superintegrable N-dimensional System, Classical and Quantum, in a Space with Variable Curvature. In M.B. Paranjape (a cura di), Quantum Theory and Symmetries: Proceedings of the 11th International Symposium, Montréal, Canada (pp. 141-148) [10.1007/978-3-030-55777-5_13].
A Confined Quasi-Maximally Superintegrable N-dimensional System, Classical and Quantum, in a Space with Variable Curvature
Ragnisco, Orlando
Writing – Original Draft Preparation
2021-01-01
Abstract
In the present paper I will briefly summarize some recent results about the solvability of the classical and quantum version of a (hyper-)spherically symmetric N-dimensional system living on a curved manifold characterized by a conformally flat metric. The system appears as a generalization of the so-called Taub–NUT system. We call it Quasi-Maximally Superintegrable (QMS) since it is endowed with 2N − 2 constants of the motion (with 2N − 1 it would have been Maximally Superintegrable (MS)) functionally independent and Poisson commuting in the Classical case, algebraically independent and commuting as operators in the Quantum case. The eigenvalues and eigenfunctions of the quantum system are explicitly given, while for the classical version we provide the analytic solution of the radial equation of motion. A few comments about the connection between exact solvability and superintegrability are made in the final part of the paper.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
