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Asymptotics for Klein—Gordon equation

  • Marin, Ana M. [1] ; Ortiz, Ruben D. [1] ; Rodriguez-Ceballos, Joel A. [2]
    1. [1] Universidad de Cartagena

      Universidad de Cartagena

      Colombia

    2. [2] Instituto Tecnológico de Morelia

      Instituto Tecnológico de Morelia

      México

  • Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 32, Nº. 3, 2013, págs. 259-265
  • Idioma: inglés
  • DOI: 10.4067/S0716-09172013000300005
  • Enlaces
  • Resumen
    • 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.

  • Referencias bibliográficas
    • Citas [1] Albeverio, S., Gesztesy, F., Høegh-Krohn, R., and Holden, H. : Solvable Models in Quantum Mechanics, Springer—Verlag, New York,...
    • [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...
    • [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,...
    • [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,...
    • [8] Zhevandrov, P., and Merzon, A. : Asymptotics of eigenfunctions in shallow potential wells and related problems, Amer. Math. Soc. Transl,...

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