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Corrections to the classical behavior of the number of bound states of Schrödinger operators. (English) Zbl 0646.35019
Let us denote by \(N_ E\) the number of bound states of the Schrödinger operator \(H=-\Delta -c/(1+| x|^ 2)+V_ 0\) below -E. \(V_ 0\) is a potential decaying at infinity sufficiently fast. We prove that, for dimension \(d=1\), \(\lim_{E\downarrow 0}(N_ E/| \ln E|)=(1/\pi)\sqrt{c-1/4}\) and for \(d=3\), \(\lim_{E\downarrow 0}(N_ E/| \ln E|)=\sum^{[\sqrt{c}-]}_{l=0}(2l+1)\sqrt{c-(l+)^ 2}\).
Reviewer: W.Kirsch

MSC:
35J10 Schrödinger operator, Schrödinger equation
35P05 General topics in linear spectral theory for PDEs
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[1] \scW. Kirsch and B. Simon, J. Funct. Anal., to appear.
[2] Müller, C., ()
[3] Reed, M.; Simon, B., ()
[4] Reed, M.; Simon, B., ()
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