We study a class of symmetric relativeiy compact perturbations satisfying ana!yticity conditions with respect to the dilatation group in R". Absence of continuous singular part for the Hamiltonians is proved together with the existence of an absolutely continuous part having spectrum [0, oo). The point spectrum consists in IR-{0} of finite multiplicity isolated energy bound-states standing in a bounded domain. Bound-state wave functions are analytic with respect to the dilatation group. Some properties of resonance poles are investigated.

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 [2e, oo), where 2 e 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.

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