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Home > Mathematics and Science Textbooks > Mathematics > Transient Tunnel Effect & Sommerfeld Problem - Waves in Semi-Infinite Structures
Transient Tunnel Effect & Sommerfeld Problem - Waves in Semi-Infinite Structures

Transient Tunnel Effect & Sommerfeld Problem - Waves in Semi-Infinite Structures


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About the Book

In this book transient waves in media with semi-infinite geometry in two significant cases are studied. The models are linear and describe 1. the collision of a relativistic massive particle with a semi-infinite potential step in one space dimension as well as 2. the diffraction of waves at a semi-infinite crack in a two-dimensional homogeneous vibrating medium (the so-called Sommerfeld Problem). For problem 1 an estimate for the L((unendlich))-time decay rate of the solution is derived which is reduced as compared with the collision free case. To this end the solution is expanded in generalized eigenfunctions and the method of stationary phase is used. The result is connected with the phenomenon of violation of causality observed for tunneling particles in recent experiments. For problem 2 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 spectral theory and the method of stationary phase are used. The results of the author solve an open problem and are an important step towards a solution formula for the transient problem.

About the Author :
Author's affiliation: Felix Ali Mehmeti, Professor, University of Valenciennes, France


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Product Details
  • ISBN-13: 9783527400829
  • Publisher: John Wiley & Sons Australia Ltd
  • Publisher Imprint: Titles Supplied by John Wiley & Sons Australia
  • Height: 243 mm
  • Weight: 5600 gr
  • ISBN-10: 3527400826
  • Publisher Date: 30 Jul 1996
  • Binding: Paperback
  • Spine Width: 10 mm
  • Width: 170 mm


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Transient Tunnel Effect & Sommerfeld Problem - Waves in Semi-Infinite Structures
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