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

Elliott H. Lieb
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Elliott H. Lieb: Princeton University, Departments of Mathematics and Physics

A chapter in Inequalities, 2002, pp 243-254 from Springer

Abstract: Abstract 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.

Keywords: Pure Math; Semigroup Property; Sharp Constant; Schr6dinger Operator; Lower Semi Continuous Function (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-3-642-55925-9_22

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