Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-16T21:16:06.423Z Has data issue: false hasContentIssue false

Eigenvalues of the Klein-Gordon equation

Published online by Cambridge University Press:  20 January 2009

Branko Najman
Affiliation:
University of Zagreb, Yugoslavia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Consider the Klein-Gordon equation

where q, Aj are real valued functions on Rn, m and e positive constants. Equation (1) describes the motion of a relativistic particle of mass m and charge e in an external field described by the electrostatic potential q and the electromagnetic potential A = (Aj); units are chosen so that the speed of light is one.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1983

References

REFERENCES

1.Bognar, J., Indefinite Inner Product Spaces (Springer, 1974).CrossRefGoogle Scholar
2.Langer, H. and Najman, B., Perturbation theory of definitizable operators, J. Op. heory, to appear.Google Scholar
3.Leinfelder, H. and Simader, C. G., Schrödinger operators with magnetic vector potential, Math. Z. 176 (1981), 120.CrossRefGoogle Scholar
4.Kato, T., Perturbation Theory for Linear Operators (Springer, 1966).Google Scholar
5.Najman, B., Wave operators and similarity for some matrix operators with applications, Glasnik Mat. 14 (34) (1979), 289307.Google Scholar
6.Najman, B., Localization of the critical points of Klein-Gordon type operators, Math. Nachr. 99 (1980), 3342.CrossRefGoogle Scholar
7.Reed, M. and Simon, B., Methods of Modern Mathematical Physics, I–IV (Academic Press).Google Scholar
8.Schechter, M., Spectra of Partial Differential Operators (North-Holland, 1971).Google Scholar
9.Simon, B., An abstract Kato's inequality for generators of positivity preserving semigroups, Indiana Univ. J. 26 (1977), 10671073.CrossRefGoogle Scholar
10.Weidmann, J., Spectral theory of partial differential operators, Proc. of Spectral Theory and Differential Equations (Lecture Notes in Mathematics 448, Springer, 1975).Google Scholar
11.Veselic, K., On the nonrelativistic limit of the bound states of the Klein-Gordon equation, J. Math. Anal. Appl., to appear.Google Scholar