Kerimov, G. A.2024-06-122024-06-1220121751-81131751-8121https://doi.org/10.1088/1751-8113/45/18/185201https://hdl.handle.net/20.500.14551/24923We apply the potential group method to a family of n-dimensional quantum Smorodinsky-Winternitz systems. The Hamiltonians of the systems are associated with first-order Casimir operators of the unitary group U(3n) restricted to certain subspaces of carrier space of the symmetric representation. Hence, the group U(3n) describes fixed energy states of a family of Smorodinsky-Winternitz systems with different potential strength. Moreover, it is shown that 2n - 1 integrals of motions (including the Hamiltonian) are related to Casimir operators of U(3n) and its subgroups.en10.1088/1751-8113/45/18/185201info:eu-repo/semantics/closedAccessDeformationsOscillatorScatteringArticle4518Q1WOS:0003036121000072-s2.0-84860320279Q2