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

Elliott Lieb

Research output: Chapter in Book/Report/Conference proceedingChapter

2 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)≤ 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.

Original languageEnglish (US)
Title of host publicationThe Stability of Matter
Subtitle of host publicationFrom Atoms to Stars: Fourth Edition
PublisherSpringer Berlin Heidelberg
Pages245-256
Number of pages12
ISBN (Print)3540420835, 9783540222125
DOIs
StatePublished - Jan 1 2005

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Fingerprint Dive into the research topics of 'The number of bound states of one-body Schroedincer operators and the Weyl problem'. Together they form a unique fingerprint.

  • Cite this

    Lieb, E. (2005). The number of bound states of one-body Schroedincer operators and the Weyl problem. In The Stability of Matter: From Atoms to Stars: Fourth Edition (pp. 245-256). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-27056-6_18