ABSTRACT
In his work [12], Mourre initiated the conjugate operator method and proved the principle of limiting absorption for three–particle systems. Since then, major progress has been made in the spectral and scattering theory for many–particle Schrödinger operators during the last decade. For example, Mourre’s result has been extended to N–particle systems by Perry–Sigal–Simon [14] and also the non–existence of positive eigenvalues has been established by Froese–Herbst [4]. Furthermore, the method has played a basic role in the proof of asymptotic completeness by Sigal–Soffer [17]. After this remarkable work, alternative proofs of asymptotic completeness have been given by several authors [5, 10, 18, 22]. In the present work, we study the spectral and scattering problems for many–particle Stark Hamiltonians with uniform electric fields by making use of the conjugate operator method. We discuss the following three problems: (1) non–existence of bound states ; (2) principle of limiting absorption ; (3) asymptotic completeness of wave operators.
