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🔗 Source: f08.uni-stuttgart.de
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Summary

Sharp spectral estimates are studied for Schrödinger operators in domains of infinite volume, with a non-negative potential V and Dirichlet conditions on the boundary. The negative spectrum consists of finitely many eigenvalues, and Riesz means of order σ are used to deduce information about the eigenvalues. The semiclasscial limit of the eigenvalues is given by the formula Rσ(λV; Ω) = Lclσ,d ∫Ω V(x) dx λσ+d/2 + o(λσ+d/2) as λ → ∞. Uniform estimates, such as the Lieb-Thirring inequalities, are used to supplement this asymptotic result, and the best constants for which these inequalities hold are found to be Lσ,d = Lclσ,d for σ ≥ 3/2.

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Sharp spectral estimates are studied for Schrödinger operators in domains of infinite volume, with a non-negative potential V and Dirichlet conditions on the...

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  • File Format: PDF
  • File Size: 525 KB
  • Pages: 28
  • Language: EN
  • Total Downloads: 100
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