Eigenvalues of Schrödinger Operators with Potential Asymptotically Homogeneous of Degree − 2

Abstract

We strengthen and generalise a result of Kirsch and Simon on the behaviour of the function NL(E), the number of bound states of the operator L = ∆ + V in Rd below −E. Here V is a bounded potential behaving asymptotically like P (ω)r−2 where P is a function on the sphere. It is well known that the eigenvalues of such an operator are all nonpositive, and… (More)

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