### Abstract

Original language | English |
---|---|

Article number | 103506 |

Number of pages | 18 |

Journal | Journal of Mathematical Physics |

Volume | 47 |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 2006 |

### Fingerprint

### Keywords

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

### Cite this

*Journal of Mathematical Physics*,

*47*(10), [103506]. https://doi.org/10.1063/1.2345108

}

*Journal of Mathematical Physics*, vol. 47, no. 10, 103506. https://doi.org/10.1063/1.2345108

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Variational principles for eigenvalues of the Klein-Gordon equation

AU - Langer, M.

AU - Tretter, Christiane

PY - 2006/10

Y1 - 2006/10

N2 - 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.

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.

KW - mathematical physics

KW - Klein-Gordon equation

KW - eigenvalues

KW - numerical mathematics

UR - http://dx.doi.org/10.1063/1.2345108

U2 - 10.1063/1.2345108

DO - 10.1063/1.2345108

M3 - Article

VL - 47

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 10

M1 - 103506

ER -