Asymptotics for Klein—Gordon equation
DOI:
https://doi.org/10.4067/S0716-09172013000300005Keywords:
Klein—Gordon equation, Asymptotics, Eigenfunctions.Abstract
We propose a simple method for constructing an asymptotic of an eigenvalue for the Klein—Gordon equation in the presence of a shallow potential well, reducing the initial problem to an integral equation and then by applying the method of Neumann series to solve it.References
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[2] Chadam, J. M. : The asymptotic behavior of the Klein-Gordon equation with external potential, J. Math. Anal. Appl., 31, pp. 334—348, (1970).
[3] Gadyl0 shin, R. : Local perturbations of the Schr¨odinger operator on the axis, Theo. Math. Phys., 132, pp. 976—982, (2002). underwater ridge.
[4] Landau, L. D., and Lifshitz, E. M. : Quantum mechanics, Pergamon, London, (1958).
[5] Schonbek, T. P. : On Inverse Scattering for the Klein-Gordon Equation, Transactions of the American Mathematical Society, 166, pp. 101—123, (1972).
[6] Simon, B. : The bound state of weakly coupled Schr¨odinger operator in one and two dimensions, Ann. Phys., 97, pp. 279—288, (1976).
[7] Synge, J. L. : A Klein-Gordon Model Particle, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 283, No. 1392, pp. 14—17, (1965).
[8] Zhevandrov, P., and Merzon, A. : Asymptotics of eigenfunctions in shallow potential wells and related problems, Amer. Math. Soc. Transl, Ser. 2. 208 (53), pp. 235—284, (2003).
How to Cite
[1]
A. M. Marin, R. D. Ortiz, and J. A. Rodriguez-Ceballos, “Asymptotics for Klein—Gordon equation”, Proyecciones (Antofagasta, On line), vol. 32, no. 3, pp. 259-265, 1.
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