4 Proof of the Adiabatic Theorem

In old quantum mechanics the adiabatic theorem established by Ehrenfest had the meaning that the quantized action variables J = n are invariant relative to an infinitely slow (adiabatic) change of a mechanical system.1 From this one can guess that if the system is in a state with definite quantum numbers before the adiabatic change started, then after the changes it will be characterized by the same quantum numbers.