A lower bound for level spacings

Elliott H. Lieb, Walter E. Thirring

Research output: Contribution to journalArticlepeer-review


We consider a single particle in a negative potential V: H = -Δ + V(x). A lower bound is found for the quantity ε{lunate}Λ - ε{lunate}, where ε{lunate} is the ground-state energy of H in all space and where ε{lunate}Λ is the ground-state energy of H in a bounded domain Λ with Dirichlet (ψ = 0) boundary conditions. Our estimate for ε{lunate}Λ - ε{lunate} involves only ε{lunate}Λ and the volume, | Λ |, but does not depend upon V or upon the shape of Λ.

Original languageEnglish (US)
Pages (from-to)88-96
Number of pages9
JournalAnnals of Physics
Issue number1
StatePublished - Jan 1977

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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