Transient Tunnel Effect and Sommerfeld Problem: Waves in Semi-Infinite Structures: 91 (Mathematical Research S.) - Softcover

Inhaltsangabe

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.

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