Marchenko equation
In mathematical physics, more specifically the one-dimensional inverse scattering problem, the Marchenko equation (or Gelfand-Levitan-Marchenko equation or GLM equation), named after Israel Gelfand, Boris Levitan and Vladimir Marchenko, is derived by computing the Fourier transform of the scattering relation: Where formula_2is a symmetric kernel, such that formula_3which is computed from the scattering data. Solving the Marchenko equation, one obtains the kernel of the transformation operator formula_4 from which the potential can be read off. This equation is derived from the Gelfand–Levitan integral equation, using the Povzner–Levitan representation.