منابع مشابه
Scattering Theory
Scattering theory is a subset of spectral theory that seeks to parametrize the absolutely continuous spectrum of an elliptic operator H on a complete manifold M with uniform structure at infinity. In the simplest case where M is compact, the spectrum of H is discrete, and scattering theory is trivial. On R, scattering theory is already non-trivial, and the techniques used in studying scattering...
متن کاملScattering Theory
A prototype of the above situation is when H is L2( — °°, °° î N), i.e., the space of square integrable functions on the whole real axis whose values lie in some accessory Hubert space Nt U(t) is translation by t, and D+ is L%(0f oo ; N). THEOREM l. If D+ is outgoing for the group U(t), then H can be represented isometrically as L%(-~ oo, oo ; N) so that U(t) is translation and D+ is the space ...
متن کاملScattering Theory
The simplest model of a scattering experiment is given by solving Schrödinger’s equation for a plane wave impinging on a localized potential. A potential V(r) might represent what a fast electron encounters on striking an atom, or an alpha particle a nucleus. Obviously, representing any such system by a potential is only a beginning, but in certain energy ranges it is quite reasonable, and we h...
متن کاملScattering theory on graphs
We consider the scattering theory for the Schrödinger operator −D2 x + V (x) on graphs made of one-dimensional wires connected to external leads. We derive two expressions for the scattering matrix on arbitrary graphs. One involves matrices that couple arcs (oriented bonds), the other involves matrices that couple vertices. We discuss a simple way to tune the coupling between the graph and the ...
متن کاملZero Range Scattering Theory
We prove here that by taking the zero range limit of conventional nonrelativistic three-particle theories and restricting the two-particle amplitude in this limit to have no singularities at negative energy .-o her than bound state poles, F we can derive unitary three particle equations depending only on two-particle physical observables. Phenom. -.. enological extensions of this theory suitabl...
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ژورنال
عنوان ژورنال: Journal of Physics G: Nuclear and Particle Physics
سال: 2003
ISSN: 0954-3899,1361-6471
DOI: 10.1088/0954-3899/29/11/013