Erik Skibsted: Absence of positive eigenvalues for hard-core N-body systems

We give an account of a recent joint work with K. Ito on absence of positive eigenvalues for generalized 2-body hard-core Schrödinger operators. We show absence of such eigenvalues 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.