منابع مشابه
Stark Effect in Lax - Phillips Scattering Theory
Abstract : The scattering theory of Lax and Phillips, originally developed to describe resonances associated with classical wave equations, has been recently extended to apply as well to the case of the Schrödinger equation in the case that the wave operators for the corresponding Lax-Phillips theory exist. It is known that the bound state levels of an atom become resonances (spectral enhanceme...
متن کاملLax-Phillips scattering theory and well-posed linear systems: a coordinate-free approach
We give a further elaboration of the fundamental connections between Lax-Phillips scattering, conservative input/state/output linear systems and Sz.-Nagy-Foias model theory for both the discreteand continuous-time settings. In particular, for the continuous-time setting, we show how to locate a scattering-conservative L2-well-posed linear system (in the sense of Staffans and Weiss) embedded in ...
متن کاملGeneralized Backscattering and the Lax-phillips Transform
Using the free-space translation representation (modified Radon transform) of Lax and Phillips in odd dimensions, it is shown that the generalized backscattering transform (so outgoing angle ω = Sθ in terms of the incoming angle with S orthogonal and Id−S invertible) may be further restricted to give an entire, globally Fredholm, operator on appropriate Sobolev spaces of potentials with compact...
متن کاملSz.-Nagy-Foias Theory and Lax-Phillips Type Semigroups in the Description of Quantum Mechanical Resonances
A quantum mechanical version of the Lax-Phillips scattering theory was recently developed. This theory is a natural framework for the description of quantum unstable systems. However, since the spectrum of the generator of evolution in this theory is unbounded from below, the existing framework does not apply to a large class of quantum mechanical scattering problems. It is shown in this work t...
متن کاملDescription of Unstable Systems in Relativistic Quantum Mechanics in the Lax-phillips Theory*
We discuss some of the experimental motivation for the need for semigroup decay laws, and the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips S-matrix. In the case of discrete (complex) spectrum of the...
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ژورنال
عنوان ژورنال: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
سال: 1981
ISSN: 0308-2105,1473-7124
DOI: 10.1017/s0308210500015158