2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/90665The problem of existence of a self-adjoint time operator conjugate to a Hamiltonian with SU(1,1) dynamical symmetry is investigated. In the space spanned by the eigenstates of the generator $K_3$ of the SU(1,1) group, the time operator for the quantum singular harmonic potential of the form $ω^2x2 + g/x2$ is constructed explicitly, and shown that it is related to the time-of-arrival operator of Aharonov and Bohm. Our construction is fully algebraic, involving only the generators of the SU(1,1) group.11 pages, LaTeX, added one new referenceQuantum Physicstext