Lowest energy states in nonrelativistic QED: Atoms and ions in motion

Michael Loss, Tadahiro Miyao, Herbert Spohn

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


Within the framework of nonrelativisitic quantum electrodynamics we consider a single nucleus and N electrons coupled to the radiation field. Since the total momentum P is conserved, the Hamiltonian H admits a fiber decomposition with respect to P with fiber Hamiltonian H (P). A stable atom, respectively ion, means that the fiber Hamiltonian H (P) has an eigenvalue at the bottom of its spectrum. We establish the existence of a ground state for H (P) under (i) an explicit bound on P, (ii) a binding condition, and (iii) an energy inequality. The binding condition is proven to hold for a heavy nucleus and the energy inequality for spinless electrons.

Original languageEnglish
Pages (from-to)353-393
Number of pages41
JournalJournal of Functional Analysis
Issue number2
StatePublished - 15 Feb 2007


  • Binding energy
  • Ground state
  • Infrared photons


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