### 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_{n}λ ^{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 _{n}f_{M} [V - α]_{-}^{n/2} for all α and V and n ≥ 3.

Original language | English (US) |
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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 | |

State | Published - Jan 1 2005 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## 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