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A systematic adiabatic perturbation theory with respect to the kinetic energyof the heavy component of a two-component quantum system is introduced. Theeffective Schr\"odinger equation for the heavy system is derived to secondorder in the inverse mass. It contains a new form of kinetic energy operatorwith a Hermitian mass tensor and a complex-valued vector potential. All of thepotentials in the effective equation can be computed without having to evaluatesums over the eigenstates of the light system. The most salient potentialapplication of the theory is to systems of electrons and nuclei. The accuracyof the theory is verified numerically in a model of a diatomic molecule andanalytically in a linear vibronic model.

Adiabatic perturbation theory for two-component systems with one heavy component