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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
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