Variational principles for eigenvalues of the Klein-Gordon equation

M. Langer, Christiane Tretter

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


In this paper variational principles for eigenvalues of an abstract model of the Klein-Gordon equation with electromagnetic potential are established. They are used to characterize and estimate eigenvalues in cases where the essential spectrum has a gap around 0, even in the presence of complex eigenvalues. As a consequence, a comparison between eigenvalues of the Klein-Gordon equation in R^d and eigenvalues of certain Schrödinger operators is obtained. The results are illustrated on examples including the Klein-Gordon equation with Coulomb and square-well potential.
Original languageEnglish
Article number103506
Number of pages18
JournalJournal of Mathematical Physics
Issue number10
Publication statusPublished - Oct 2006


  • mathematical physics
  • Klein-Gordon equation
  • eigenvalues
  • numerical mathematics


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