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.

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