Time-Evolution of the Coherent and the Squeezed States of Many-Body Systems Based on the Basic Idea of the Boson Mapping and the TDHF Method

Various works performed by the present authors in the 1990s are reviewed. The topics discussed in this paper are mainly related to the time-evolution of the coherent and the squeezed states of the systems obeying the su(2)- and the su(1,1)-algebra. The formulations are based on the basic idea of the boson mapping and the TDHF theory in canonical form. Under the time-dependent variational procedure for trial states appropriately chosen, the time-evolution of the systems under investigation is described. Further, it is shown that this method enables us to obtain the classical counterparts of the original quantal systems.