  The problem of resonant generation of nonground-state condensates is
addressed aiming at resolving the seeming paradox that arises when one resorts
to the adiabatic representation. In this picture, the eigenvalues and
eigenfunctions of a time-dependent Gross-Pitaevskii Hamiltonian are also
functions of time. Since the level energies vary in time, no definite
transition frequency can be introduced. Hence no external modulation with a
fixed frequency can be made resonant. Thus, the resonant generation of
adiabatic coherent modes is impossible. However, this paradox occurs only in
the frame of the adiabatic picture. It is shown that no paradox exists in the
properly formulated diabatic representation. The resonant generation of
diabatic coherent modes is a well defined phenomenon. As an example, the
equations are derived, describing the generation of diabatic coherent modes by
the combined resonant modulation of the trapping potential and atomic
scattering length.
