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Completeness of stationary scattering states. I

✍ Scribed by N.G. Van Kampen

Book ID
104162233
Publisher
Elsevier Science
Year
1954
Weight
409 KB
Volume
21
Category
Article
ISSN
0031-8914

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✦ Synopsis

From this one finds for g+(z) = q(z)/p(z)

This function can be directly checked to be a solution of (I 1), so that in the case (21) the set (1) is not complete.

πŸ“œ SIMILAR VOLUMES

Completeness of stationary scattering st
Completeness of stationary scattering states. II
✍ N.G. Van Kampen πŸ“‚ Article πŸ“… 1955 πŸ› Elsevier Science βš– 496 KB

This result could also be obtained by using in the work of the previous section other solutions of {25) than ( ). The special solution ( ) is uniquely characterized by the property that S0{x)/0\_(x) belongs to ~\_. Indeed, a solution ho\_(x) of the homogeneous equation cannot have this same property

Completeness of scattering states for ro
Completeness of scattering states for rough interfaces
✍ David H. Berman πŸ“‚ Article πŸ“… 1992 πŸ› Elsevier Science 🌐 English βš– 853 KB

Using energy conservation and causality considerations, the completeness of scattering states is established for plane waves impinging on an irregular interface. Provided certain limiting operations commute with differentiation, it is shown that surface waves need not be explicitly included in the W

Linear passive stationary scattering sys
Linear passive stationary scattering systems with Pontryagin state spaces
✍ D. Z. Arov; J. Rovnyak; S. M. Saprikin πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 329 KB

## Abstract Passive scattering systems having Pontryagin state spaces and their minimal conservative dilations are investigated. The transfer functions of passive scattering systems are generalized Schur functions. In the case of a simple conservative system, the right and left KreΔ­n–Langer factori