Exactly solvable models with time-dependent potentials

A method of constructing a time-dependent periodic Hamiltonian is elaborated for which a system of Schrodinger equations admits analytic solutions. Time-independent soluble problems are transformed into time-dependent ones by a set Of unitary time dependent transformations and a proper choice of initial states. A new class of 2 x 2 periodic time-dependent Hamiltonians with cyclic solutions is constructed in a closed analytic form. In particular, the periodic time-dependent Hamiltonians are generated whose expectation values for cyclic solutions and spin-expectation values do not depend on time. As a consequence, this approach can be used for modelling quantum dynamic wells and wires with the effect of the particle localization. (C) 2003 Elsevier Science B.V. All rights reserved.