Article

The inverse scattering problem at fixed energy based on the Marchenko equation for an auxiliary Sturm-Liouville operator

05/2012; DOI:10.1088/1751-8113/46/4/045303
Source: arXiv

ABSTRACT A new approach is proposed to the solution of the quantum mechanical inverse
scattering problem at fixed energy. The method relates the fixed energy phase
shifts to those arising in an auxiliary Sturm-Liouville problem via the
interpolation theory of the Weyl-Titchmarsh m-function. Then a Marchenko
equation is solved to obtain the potential.

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Keywords

auxiliary Sturm-Liouville problem
 
interpolation theory
 

Tamas Palmai