  Under the assumption that every material object can ultimately be described
by quantum theory, we ask how a probe system evolves in a device prepared and
kept in a superposition state of values of its classical parameter. We find
that, under ideal conditions, the evolution of the system would be unitary,
generated by an effective Hamiltonian. We describe also an incoherent use of
the device that achieves the same effective evolution on an ensemble. The
effective Hamiltonian thus generated may have qualitatively different features
from that associated to a classical value of the parameter.
