an:03888213
Zbl 0557.35094
Yafaev, D. R.
On resonance scattering by a negative potential
RU
Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 138, 184-193 (1984).
00221113
1984
j
35Q99 35P25 81U99
potential with compact support; quantum scattering; lower estimate; positive repulsive potential
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.