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On the applicability of the Lippmann-Schwinger approach to the scattering of particles by semiinfinite crystals

✍ Scribed by R.F Alvarez-Estrada; M.E Villalon

Publisher: Elsevier Science
Year: 1978
Tongue: English
Weight: 629 KB
Volume: 111
Category: Article
ISSN: 0003-4916
DOI: 10.1016/0003-4916(78)90229-4

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✦ Synopsis

We present a formal approach, using integral equations of the LippmannSchwinger type, to the scattering of particles by semiinfinite periodic potentials. The two possible physical situations, scattering of free plane waves and scattering of Bloch waves, are treated with two1 different integral equations. The validity of this formalism to describe the particle wavefunction in the whole space is established, and its connection with the matching method is studied. The corresponding extinction theorems, one for each situation, are derived. Interesting relations among the probability amplitudes for both scattering problems are found.

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