The number of bound states of one-body Schroedincer operators and the Weyl problem

Elliott H. Lieb

doi:10.1007/3-540-27056-6_18

The number of bound states of one-body Schroedincer operators and the Weyl problem

Elliott H. Lieb

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

3 Scopus citations

Abstract

If Ñ(Ω, λ) is the number of eigenvalues of -Δ in a domain Ω In a suitable Rieinannian manifold of dimension n, we derive bounds of the form Ñ (Ω,λ)≤ D_nλ ^n/2 |Ω| for all Ω, λ, n, Likewise, if N _α (V) is the number of nonpositive eigenvalues of -Δ + V(x) which are ≤ α ≤ 0, then N_α(V)≤ L _nf_M [V - α]_-^n/2 for all α and V and n ≥ 3.

Original language	English (US)
Title of host publication	The Stability of Matter
Subtitle of host publication	From Atoms to Stars: Fourth Edition
Publisher	Springer Berlin Heidelberg
Pages	245-256
Number of pages	12
ISBN (Print)	3540420835, 9783540222125
DOIs	https://doi.org/10.1007/3-540-27056-6_18
State	Published - 2005

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

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10.1007/3-540-27056-6_18

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title = "The number of bound states of one-body Schroedincer operators and the Weyl problem",

abstract = "If {\~N}(Ω, λ) is the number of eigenvalues of -Δ in a domain Ω In a suitable Rieinannian manifold of dimension n, we derive bounds of the form {\~N} (Ω,λ)≤ Dnλ n/2 |Ω| for all Ω, λ, n, Likewise, if N α (V) is the number of nonpositive eigenvalues of -Δ + V(x) which are ≤ α ≤ 0, then Nα(V)≤ L nfM [V - α]-n/2 for all α and V and n ≥ 3.",

author = "Lieb, {Elliott H.}",

year = "2005",

doi = "10.1007/3-540-27056-6_18",

language = "English (US)",

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T1 - The number of bound states of one-body Schroedincer operators and the Weyl problem

AU - Lieb, Elliott H.

PY - 2005

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N2 - If Ñ(Ω, λ) is the number of eigenvalues of -Δ in a domain Ω In a suitable Rieinannian manifold of dimension n, we derive bounds of the form Ñ (Ω,λ)≤ Dnλ n/2 |Ω| for all Ω, λ, n, Likewise, if N α (V) is the number of nonpositive eigenvalues of -Δ + V(x) which are ≤ α ≤ 0, then Nα(V)≤ L nfM [V - α]-n/2 for all α and V and n ≥ 3.

AB - If Ñ(Ω, λ) is the number of eigenvalues of -Δ in a domain Ω In a suitable Rieinannian manifold of dimension n, we derive bounds of the form Ñ (Ω,λ)≤ Dnλ n/2 |Ω| for all Ω, λ, n, Likewise, if N α (V) is the number of nonpositive eigenvalues of -Δ + V(x) which are ≤ α ≤ 0, then Nα(V)≤ L nfM [V - α]-n/2 for all α and V and n ≥ 3.

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M3 - Chapter

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SN - 3540420835

SN - 9783540222125

SP - 245

EP - 256

BT - The Stability of Matter

PB - Springer Berlin Heidelberg

ER -

The number of bound states of one-body Schroedincer operators and the Weyl problem

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