Marchenko equation

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In mathematical physics, the Marchenko equation is a solution of the inverse scattering problem, when we vary only the energy of the input particle and the impact parameter b is constant.

The main equation is:

K(r,r')+g(r,r')+\int_r^{\infty}K(r,r'')g(r'',r')dr''=0

where

g(r,r')

is a symmetric kernel, so that

g(r,r') = g = (r',r).

The equation is derived from the Gel'fand-Levitan integral equation, using the Povzner-Levitan representation.

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