Summary
Potential scattering of a non-relativistic particle is studied by means of the Born series for the Green’s function, wave function, and scattering amplitude. For a wide class of potentials, these series are proved to converge at sufficiently high incident energies. The validity of the Born approximation in the high energy limit is also shown.
Riassunto
Lo scattering potenziale di una particella non relativistica si studia servendosi della serie di Born per la funzione di Green, la funzione d’onda e l’ampiezza di scattering. Si prova che per un’ampia classe di potenziali queste serie convergono per energie incidenti sufficientemente elevate. Si dimostra anche la validità dell’approssimazione di Born nel campo delle alte energie.
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References
M. Born:Zeits. f. Phys.,38, 803 (1926).
R. Jost andA. Pais:Phys. Rev.,82, 840 (1951). See, also,W. Kohn:Rev. Mod. Phys. 26, 292 (1954).
See, for example, the methods ofE. C. Titchmarch:Theory of functions, Chap. X and Sect. 12.2 (Oxford, 1939).
See, for example,P. M. Morse andH. Feshbach:Methods of Theoretical Physics. (New York, 1953), p. 661.
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Zemach, C., Klein, A. The born expansion in non-relativistic quantum theory. Nuovo Cim 10, 1078–1087 (1958). https://doi.org/10.1007/BF02859570
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DOI: https://doi.org/10.1007/BF02859570