Langer, M. and Tretter, Christiane (2006) *Variational principles for eigenvalues of the Klein-Gordon equation.* Journal of Mathematical Physics, 47 (10). pp. 1-18. 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.

Item type: | Article |
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ID code: | 4553 |

Keywords: | mathematical physics, Klein-Gordon equation, eigenvalues, numerical mathematics, Mathematics, Physics, Mathematical Physics, Statistical and Nonlinear Physics |

Subjects: | Science > Mathematics Science > Physics |

Department: | Faculty of Science > Mathematics and Statistics |

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Depositing user: | Strathprints Administrator |

Date Deposited: | 01 Nov 2007 |

Last modified: | 28 Mar 2014 10:55 |

URI: | http://strathprints.strath.ac.uk/id/eprint/4553 |

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