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Variational principles for eigenvalues of the Klein-Gordon equation

Langer, M. and Tretter, Christiane (2006) Variational principles for eigenvalues of the Klein-Gordon equation. Journal of Mathematical Physics, 47 (10). ISSN 0022-2488

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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.