# zbMATH — the first resource for mathematics

Some problems in inverse scattering theory. (English) Zbl 0641.35053
Journ. Équ. Dériv. Partielles, St.-Jean-De-Monts 1987, Exp. No. 3, 3 p. (1987).
We shall consider the Schrödinger operator $$H_ v=-\Delta +v(x)$$ in $${\mathbb{R}}^ n$$, where $$n=3,5,...$$. We assume that $$v\in \nu$$, i.e. $(1)\quad \int (1+| x|)^{| \alpha | -(n-2)}| v^{(\alpha)}(x)| dx<\infty$ for any $$\alpha$$.
Some of the main problems we consider are the following:
(a) Analysis of bound states and poles of the scattering matrix.
(b) Backward scattering.
(c) The characterization problem for scattering matrices.
This talk will be a continuation of the author’s lecture at École Polytechnique [Semin., Equations Deriv. Partielles 1986-1987, 6 p. (1987)], and we shall mainly give some comments to (a).

##### MSC:
 35P25 Scattering theory for PDEs 35J10 Schrödinger operator, Schrödinger equation 35R30 Inverse problems for PDEs
Full Text: