On the analytic properties of nonrelativistic two-body off-shell amplitudes. II. Off-shell generalizations of the jost formalism: J. Y. Pasquier, Laboratoire de Physique Théorique et Hautes Énergies, Université Paris-Sud, Orsay, France, and R. Pasquier, Institut de Physique Nucléaire, Division de Physique Théorique, Orsay, France

• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 82 KB
• Volume: 110
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(78)90049-0

✦ 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.