Variational principles for eigenvalues of the Klein-Gordon equation

M. Langer, Christiane Tretter

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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
Volume47
Issue number10
DOIs
Publication statusPublished - Oct 2006

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Klein-Gordon equation
Klein-Gordon Equation
variational principles
Variational Principle
eigenvalues
Eigenvalue
Eigenvalue Estimates
Essential Spectrum
Potential Well
square wells
electromagnetism
Operator
operators
estimates
Model

Keywords

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

Cite this

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Variational principles for eigenvalues of the Klein-Gordon equation. / Langer, M.; Tretter, Christiane.

In: Journal of Mathematical Physics, Vol. 47, No. 10, 103506, 10.2006.

Research output: Contribution to journalArticle

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AB - 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.

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KW - eigenvalues

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