ON THE LANDAU-ZENER FORMULA FOR 2-LEVEL SYSTEMS

It is shown that the transition probability between eigenstates of a t ime-dependent two-level system is given by the Fourier transform in th e adiabatic parameter of a function determined by the Hamiltonian. Suf ficient and necessary conditions for the transition probability betwee n levels to decrease exponentially in the adiabatic limit are establis hed. Our method involves a Paley-Wiener type theorem to study the Four ier transform of functions belonging to a Hardy class on a strip.