## Marchenko inversion for perturbations. II: Inclusion of bound states.(English)Zbl 0641.35069

[For Part I see the preceding review.]
The Marchenko inversion method of the one-dimensional non-relativistic quantum mechanics is generalized to perturbations when the bound states are present. The change in the potential that corresponds to a finite change in the scattering matrix is given as a sum of two terms. The first term, not related to the bound states, is obtained from the solution to a Marchenko equation for perturbations and the second term is related to the bound states.

### MSC:

 35Q99 Partial differential equations of mathematical physics and other areas of application 81U20 $$S$$-matrix theory, etc. in quantum theory 35R30 Inverse problems for PDEs 35P25 Scattering theory for PDEs

Zbl 0641.35068
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