  We introduce a new class of quantum models with time-dependent Hamiltonians
of a special scaling form. By using a couple of time-dependent unitary
transformations, the time evolution of these models is expressed in terms of
related systems with time-independent Hamiltonians. The mapping of dynamics can
be performed in any dimension, for an arbitrary number of interacting particles
and for any type of the scaling interaction potential. The exact solvability of
a "dual" time-independent Hamiltonian automatically means the exact solvability
of the original problem with model time-dependence.
