Transient tunnel effect and Sommerfeld problem : waves in semi-infinite structures
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Bibliographic Information
Transient tunnel effect and Sommerfeld problem : waves in semi-infinite structures
（Mathematical research = Mathematische Forschung, v. 91）
Akademie Verlag, c1996
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Note
Includes bibliographical references (p. [199]-210)
Description and Table of Contents
Description
This volume investigates transient waves in media with semi-infinite geometry in two significant cases: the collision of a relativistic massive particle with a semi-infinite potential step in one space dimension; and the defraction of waves at a semi-infinite crack in a two-dimensional homogeneous vibrating medium (the so-called Sommerfield Problem). For the first problem, an estimate for the infinity-time decay rate of the solution is derived which is reduced as compared with the collision freee case. For problem two, for real wave numbers, a representation of stationary solutions in terms of generalized eigenfunctions and a limiting absorption principle are obtained. Formulae by E. Meister and F.O. Speck for the absorption case, uncertainty principles for Laplace integrals, features of special theory and the method of stationary phase are used. The results of the author solve an open problem and are a step towards a solution for the transient problem.
Table of Contents
- Spectral Theory and LN- Decay for the Klein-Gordon Equation with Potential Step - The Tunnerl Effect: Expansion in Generalized Eigenfunctions
- Time Decay
- Physical Interpretations
- A Limiting Absorption Principle for the Sommerfeld Problem in the Plane: The Resolvent for Real Wave Numbers
- Generalized Eigenfunctions as Laplace Integrals
- A Limiting Absorption Principle and its Convergence Speed.
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