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A class of analytic perturbations for one-body Schrödinger Hamiltonians


We study a class of symmetric relatively compact perturbations satisfying analyticity conditions with respect to the dilatation group inR n. Absence of continuous singular part for the Hamiltonians is proved together with the existence of an absolutely continuous part having spectrum [0, ∞). The point spectrum consists in R−{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.

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Aguilar, J., Combes, J.M. A class of analytic perturbations for one-body Schrödinger Hamiltonians. Commun.Math. Phys. 22, 269–279 (1971).

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