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Absence of positive eigenvalues for hard-core N-body systems

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We show absence of positive eigenvalues for generalized 2-body hard-core Schrödinger operators under the condition of bounded strictly convex obstacles. A scheme for showing absence of positive eigenvalues for generalized N-body hard-core Schrödinger operators, N≥ 2, is presented. This scheme involves high energy resolvent estimates, and for N=2 it is implemented by a Mourre commutator type method. A particular example is the Helium atom with the assumption of infinite mass and finite extent nucleus.
Original languageEnglish
PublisherDepartment of Mathematics, Aarhus University
Number of pages41
Publication statusPublished - 2012

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