New classes of analytic solutions of the three-state problem

A rich multiparametric class of solutions of the time-dependent Schrodinger equations, including many integrable cases known at present of the three-state problem, is derived. In addition, the class contains an infinite number of new multiparametric integrable subfamilies. Examples of such four-parametric new subfamilies of asymmetric, in general, amplitude and frequency modulation functions permitting solution of the three-state problem in terms of the Clausen function are presented.