×

zbMATH — the first resource for mathematics

On resonance scattering by a negative potential. (Russian. English summary) Zbl 0557.35094
Summary: The dependence on a coupling constant \(g>0\) of the total cross-section \(\sigma\) (g) (at a fixed energy of a particle) for quantum scattering by a potential \(g\bigvee (x)\) with a compact support is considered. It is found that for a central potential with a nontrivial negative part \(\sigma\) (g) is unbounded for some sequence \(g_{l}\to \infty\). Moreover, the lower estimate \(\sigma (g_{l})\geq Cg^{1/2}_{l}\), \(C>O\), holds. On the contrary, for a positive repulsive potential (not necessarily central) the total cross-section is shown to be bounded uniformly in g.

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
35P25 Scattering theory for PDEs
81U99 Quantum scattering theory
PDF BibTeX XML Cite
Full Text: DOI EuDML