SU(1,1) Lie algebra applied to the time-dependent quadratic Hamiltonian system perturbed by a singularity

We realized SU(1,1) Lie algebra in terms of the appropriate SU(1:1) generators for the time-dependent quadratic Hamiltonian system perturbed by a singularity. Exact quantum states of the system are investigated using SU(1,1) Lie algebra. Various expectation values in two kinds of the generalized SU(1,1) coherent states, that, is, BG coherent, states and Perelomov coherent states are derived. We applied our study to the CKOPS (Caldirola-Kanai oscillator perturbed by a singularity). Due to the damping constant gamma, the probability density of the SU(1,1) coherent states for the CKOPS converged to the center with time. The time evolution of the probability density in SU(1,1) coherent states for the CKOPS are very similar to the classical trajectory.