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Stability of the Marchenko inversion. (English) Zbl 0641.35070

The stability of the Marchenko inversion in the one-dimensional non- relativistic quantum mechanics is studied. First, two bounds on the integral of the potential difference are given in terms of the integral of the difference in the scattering matrix. Second, a pointwise bound on the potential difference is obtained. Finally, the estimates are refined for the case of two scattering matrices coinciding on the finite energy interval \(k\in [0,N]\).

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35B35 Stability in context of PDEs
81U20 \(S\)-matrix theory, etc. in quantum theory
35R30 Inverse problems for PDEs
35P25 Scattering theory for PDEs
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