Marchenko equation
Encyclopedia
In mathematical physics
, the Marchenko equation is a solution of the inverse scattering problem
, when the energy of the input particle is a variable, and the impact parameter
b is constant.
The main equation is:
where
is a symmetric kernel, so that
This equation is derived from the Gel'fand-Levitan integral equation, using the Povzner-Levitan representation.
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
, the Marchenko equation is a solution of the inverse scattering problem
Inverse scattering problem
In the physics field of of scattering theory, the inverse scattering problem is that of determining characteristics of an object based on data of how it scatters incoming radiation or particles....
, when the energy of the input particle is a variable, and the impact parameter
Impact parameter
The impact parameter b is defined as the perpendicular distance between the path of a projectile and the center of the field U created by an object that the projectile is approaching...
b is constant.
The main equation is:
where
is a symmetric kernel, so that
This equation is derived from the Gel'fand-Levitan integral equation, using the Povzner-Levitan representation.