SL(2) VARIATIONAL SCHEMES FOR SOLVING ONE CLASS OF NONLINEAR QUANTUM MODELS

Hamiltonians of a wide-spread class of Gi, invariant nonlinear quantum models, including multiboson and frequency conversion ones, are expre ssed as nonlinear functions of sl(2) generators. This enables us to us e variational schemes, based on sl(2) generalized coherent states as t rial functions, to obtain new (sl(2) cluster) quasi-classical solution s of spectral and evolution tasks which smoothly approximate exact one s and catch explicitly quantum cooperative features of the models unde r study (in contrast with standard independent-mode quasi-classical ap proximations). In such a way new analytical expressions are found for the energy spectra which are beyond both equidistant and quasi-equidis tant ones obtained earlier. (C) 1998 Elsevier Science B.V.