A novel approach to estimate the stability of onedimensional quantum inverse scattering
Abstract
We present a novel method to estimate the stability of the Marchenko equation for finite datasets. We show that we can derive a recursion relationship for the Fourier expansion coefficients of the kernel which is solved by the Marchenko equation. The method can easily be implemented numerically. Moreover, we discus the stability of the onedimensional inverse scattering problem by using Lyapunov exponents. We give conditions on the scattering data to provide stable inversion results. A numerical example is given.
 Publication:

arXiv eprints
 Pub Date:
 August 1998
 DOI:
 10.48550/arXiv.mathph/9808008
 arXiv:
 arXiv:mathph/9808008
 Bibcode:
 1998math.ph...8008D
 Keywords:

 Mathematical Physics;
 Mathematics  Mathematical Physics;
 Mathematics  Numerical Analysis
 EPrint:
 10 pages Latex, figures available upon request or on http://asterix.urc.tue.nl/~elechd/abstr13.html