TIME EVOLUTION OF QUANTUM-SYSTEMS WITH TIME-DEPENDENT HAMILTONIAN ANDTHE INVARIANT HERMITIAN OPERATOR

We study the time evolution of a class of exactly solvable time-depend ent quantum systems with a time-dependent Hamiltonian given by a linea r combination of SU(1, 1) and SU(2) generators with the help of the in variant Hermitian operator. The exact common solutions of the Schrodin ger equations for both the SU(1, 1) and SU(2) systems are obtained in terms of eigenstates of the invariant operator. The adiabatic and non- adiabatic Berry phases are calculated with the exact solutions. Moreov er, we derive an explicit time-evolution operator which is used to inv estigate the time-dependent two-photon squeezing states and SU(2) sque ezing states. The squeezing properties of the time-dependent SU(1, 1) coherent stales are also discussed.