Family of N-dimensional superintegrable systems and quadratic algebra structures

摘要

Abstract. Classical and quantum superintegrable systems have a long history and they possess more integrals of motion than degrees of freedom. They have many attractive properties, wide applications in modern physics and connection to many domains in pure and applied mathematics. We overview two new families of superintegrable Kepler-Coulomb systems with non-central terms and superintegrable Hamiltonians with double singular oscillators of type (n, N - n) in N -dimensional Euclidean space. We pr.