  We show that the origin of the nonequivalence of Hamiltonians in different
representations is a change of the form of the time-derivative operator at a
time-dependent unitary transformation. This nonequivalence does not lead to an
ambiguity of the energy expectation values of a particle in nonstationary
fields but assigns the basic representation. It has been explicitly or
implicitly supposed in previous investigations that this representation is the
Dirac one. We prove the alternative assertion about the basic role of the
Foldy-Wouthuysen representation. We also derive the general equation for the
energy expectation values in the Dirac representation. As an example, we
consider a spin-1/2 particle with anomalous magnetic and electric dipole
moments in strong time-dependent electromagnetic fields. We apply the obtained
results to a spin-1/2 particle in a plane monochromatic electromagnetic wave
and give an example of the exact Foldy-Wouthuysen transformation in the
nonstationary case.
