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Zur physikalischen Interpretation von Polen der Jost‐Funktionen
Author(s) -
Kilian H.
Publication year - 1968
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19684760705
Subject(s) - physics , complex plane , scattering , mathematical physics , interpretation (philosophy) , plane (geometry) , resonance (particle physics) , class (philosophy) , quantum mechanics , mathematical analysis , mathematics , geometry , artificial intelligence , computer science , programming language
We consider a class of potentials V ( r ) fullfilling the usual momentum requirements, which lead to a pole of the JOST functions f 1 ( k ) ( 1 = 0, 1, 2,…) at any given point in the upper half of the complex k ‐plane. These poles are on the one hand intimately connected to the asymptotic behaviour of V ( r ) for large r and may on the other hand lead to a certain type of resonance in the neighbourhood of which the scattering phase shift varies rapidly downwards. Comparing these JOST functions to those obtained for the Potentials V R which arise by cutting V ( r ) off for r > R we discuss the physical interpretability of the analytical properties of JOST functions in the upper half of the complex k ‐plane. We are thus finally lead o consider a certain pole approximation to describe form elastic scattering analogous to WIGNER's single level approximation for compound elastic scattering.