Semiclassical Szegö limit of resonance clusters for the hydrogen atom Stark Hamiltonian

Peter D. Hislop, Carlos Villegas-Blas

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We study the weighted averages of resonance clusters for the hydrogen atom with a Stark electric field in the weak field limit. We prove a semiclassical Szegö-type theorem for resonance clusters showing that the limiting distribution of the resonance shifts concentrates on the classical energy surface corresponding to a rescaled eigenvalue of the hydrogen atom Hamiltonian. This result extends Szegö-type results on eigenvalue clusters to resonance clusters. There are two new features in this work: first, the study of resonance clusters requires the use of non-self-adjoint operators, and second, the Stark perturbation is unbounded so control of the perturbation is achieved using localization properties of coherent states corresponding to hydrogen atom eigenvalues.

Original languageEnglish
Pages (from-to)17-44
Number of pages28
JournalAsymptotic Analysis
Issue number1-2
StatePublished - 2012


  • hydrogen atom Stark effect
  • resonance clusters
  • semiclassical Szegö limit

ASJC Scopus subject areas

  • General Mathematics


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