  A systematic adiabatic perturbation theory with respect to the kinetic energy
of the heavy component of a two-component quantum system is introduced. The
effective Schr\"odinger equation for the heavy system is derived to second
order in the inverse mass. It contains a new form of kinetic energy operator
with a Hermitian mass tensor and a complex-valued vector potential. All of the
potentials in the effective equation can be computed without having to evaluate
sums over the eigenstates of the light system. The most salient potential
application of the theory is to systems of electrons and nuclei. The accuracy
of the theory is verified numerically in a model of a diatomic molecule and
analytically in a linear vibronic model.

Quantum Physics;Other Condensed Matter