Spectral properties of many-body Schrödinger operators with dilatation-analytic interactions

Abstract

Quantum mechanical N-body systems with dilatation analytic interactions are investigated. Absence of continuous singular part for the Hamiltonians is proved together with the existence of an absolutely continuous part having spectrum [λe, ∞), where λe is the lowest many body threshold of the system. In the complement of the set of thresholds the point spectrum is discrete; corresponding bound state wave-functions are analytic with respect to the dilatation group. © 1971 Springer-Verlag.