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Marchenko inversion for perturbations: I. (English) Zbl 0641.35068

[For part II see the review below.]
The Marchenko inversion method of the one-dimensional non-relativistic quantum mechanics is generalized to perturbations. The change in the potential that corresponds to a finite change in the scattering matrix is obtained by formulating a Marchenko-like integral equation. The method used here may be generalizable to higher dimensions because the inversion is formulated in terms of scattering matrices, not only in terms of reflection coefficients.

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

Citations:

Zbl 0641.35069
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