Eigenvalues of Schrödinger operators with potential asymptotically homogeneous of degree -2
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 = Δ+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 accumulate only at 0. If the operator ΔSd-1 +P on the sphere Sd-1 has negative eigenvalues -μ1, ⋯ ,-μn less than -(d-2)2/4, we prove that NL(E) may...[Show more]
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|Source:||Transactions of the American Mathematical Society|
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