Inequalities pp 243-254 | Cite as

The Number of Bound States of One-Body Schroedinger Operators and the Weyl Problem

  • Elliott H. Lieb


If N ((Ω,λ) is the number of eigenvalues of -Δ in a domain Ω, in a suitable Riemannian manifold of dimension n, we derive bounds of the form \(\tilde N(\Omega ,\lambda ) \le {D_n}{\lambda ^{n/2}}\left| \Omega \right|\) for all Ω, * , n , Likewise, if N03B1; (V) is the number of nonpositive eigenvalues of -Δ + V (x) which are ≤ a ≤ 0, then \({N_\alpha }(V) \le {L_n}\int {_M} \left[ {V - \alpha } \right]_\_^{n/2}\) for all α and V and n ≥ 3. 1980 Mathematics Subject Classification 35P15.


Pure Math Semigroup Property Sharp Constant Schr6dinger Operator Lower Semi Continuous Function 
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© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Elliott H. Lieb
    • 1
  1. 1.Departments of Mathematics and PhysicsPrinceton UniversityPrincetonUSA

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