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On uniform approximations to the solutions of the partial-wave Lippman-Schwinger equation

Об однородных приближениях для решений парциального уравнения Липпмана-Швингера

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Il Nuovo Cimento A (1965-1970)

Summary

The partial-wave Lippman-Schwinger equation for a superposition of Yukawa potentials for two specific forms of the weight function is reduced to infinite systems of linear (algebraic) equations for the two cases considered. It is shown that the linear transformations which these systems of linear equations define are compact in Hilbert space for physical values of the energy.

Riassunto

Si riduce l'equazione d'onda parziale di Lippman-Schwinger per una sovrapposizione di potenziali di Yukawa per due forme specifiche della funzione di ponderazione a sistemi infiniti di equazioni (algebriche) lineari per i due casi considerati. Si dimostra che le trasformazioni lineari, definite da questi sistemi di equazioni lineari, sono compatte nello spazio di Hilbert per valori fisici dell'energia.

Резюме

Парциальное уравнение Липпмана-Швингера для суперпозиции потенциалов Юкавы для двух специальных форм весовой функции сводится к бесконечным системам линейных (алгебраических) уравнений для двух рассмотренных случаев. Показывается, что линейные преобразования, которые эти системы линейных уравнений определяют, являются компактными в пространстве Гильберта для физических значений чнергии.

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References

  1. See the extensive literature quoted inC. Lovelace:Phys. Rev.,135, B 1225 (1964).

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  2. Higher Transcendental Functions, Bateman Manuscript Project, vol. 1 (New York, 1953), p. 154.

  3. Tables of Integral Transforms, Bateman Manuscript Project, vol. 2 (New York, 1954), p. 251.

  4. Tables of Integral Transforms, Bateman Manuscript Project, vol. 1 (New York, 1954), p. 310.

  5. See, for instance,A. E. Taylor:Introduction to Functional Analysis (New York, 1958), p. 286.

  6. W. Rudin:Principles of Mathematical Analysis, II ed. (New York, 1964), p. 93.

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Authors and Affiliations

  1. Department of Applied Mathematics, The University of Hull, Hull

    M. H. Choudhury

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  1. M. H. Choudhury
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Traduzione a cura della Redazione.

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Choudhury, M.H. On uniform approximations to the solutions of the partial-wave Lippman-Schwinger equation. Nuovo Cimento A (1965-1970) 57, 601–616 (1968). https://doi.org/10.1007/BF02751369

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  • DOI: https://doi.org/10.1007/BF02751369

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