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
Full Text: