On the applicability of the Lippmann-Schwinger approach to the scattering of particles by semi-infinite crystals: R. F. Alvarez-Estrada, Departamento de Física Teórica, Facultad de Ciencias Físicas, Universidad Complutense, Madrid-3, Spain; and M. E. Villalon, Division Física de Radiaciones, Junta de Energía Nuclear, Madrid-3, Spain

• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 82 KB
• Volume: 110
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(78)90046-5

✦ Synopsis

We present a formal approach, using integral equations of the Lippmann-Schwinger type, to the scattering of particles by semiinlinite periodic potentials. The two possible physical situations, scattering of free plane waves and scattering of Bloch waves, are treated with two 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.

The Time-Energy Uncertainty Relation.