Exact Solutions for the General Nonstationary Oscillator with a Singular Perturbation

Three linearly independent Hermitian invariants for the nonstationary generalized singular oscillator (SO) are constructed and their complex linear combination is diagonalized. The constructed family of eigenstates contains as subsets all previously obtained solutions for the SO and includes all Robertson and Schr\"odinger intelligent states for the three invariants. It is shown that the constructed analogues of the SU(1,1) group-related coherent states for the SO minimize the Robertson and Schr\"odinger relations for the three invariants and for every pair of them simultaneously. The squeezing properties of the new states are briefly discussed.