The adiabatic approximation in the theory of molecules and solids

Abstract A critical reconsideration of the adiabatic approximation as a basis of molecular and solid state physics is made. The first part of the paper is devoted to the general theory of the adiabatic approach to the solution of the energy eigenvalue problem. The relations between the basic (dynamic) and the crude (static) adiabatic approximations are discussed. In particular, use is made of the two-state model for non-degenerate and nearly degenerate states. The second part deals with the applications of the adiabatic approach to the theory of quantum transitions in molecular systems (including crystals) with particular emphasis on non-radiative processes. Both the semiclassical and the quantum-mechanical theories of these processes are considered in detail making use of two-state models. On the basis of the main results of the. two parts of the paper a general discussion is made on the various aspects of the recent criticism of the adiabatic approach.