  A generalized formalism of the so-called non-adiabatic quantum molecular
dynamics is presented, which applies for atomic many-body systems in external
laser fields. The theory treats the nuclear dynamics and electronic transitions
simultaneously in a mixed classical-quantum approach. Exact, self-consistent
equations of motion are derived from the action principle by combining
time-dependent density functional theory in basis expansion with classical
molecular dynamics. Structure and properties of the resulting equations of
motion as well as the energy and momentum balance equations are discussed in
detail. Future applications of the formalism are briefly outlined.
