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 Volodymyr Marchenko, is derived by computing the Fourier transform of the scattering relation:

is a symmetric kernel from which the potential can be read off. This equation is derived from the Gelfand–Levitan integral equation, using the Povzner–Levitan representation.

Application to scattering theory

for the Schrödinger operator, one has the scattering are from the discrete bound spectrum.

See also

• Lax pair

Notes

References