Greenfüggvény

Greenfüggvény is a term of German origin, literally translating to "Green function". In physics and mathematics, a Green's function is a specific solution to a non-homogeneous linear differential equation with given boundary conditions. It is named after the mathematician George Green.

The fundamental idea behind Green's functions is that if one knows the response of a linear system to a point source or impulse (represented by the Green's function), then the response to any arbitrary source can be found by integrating the Green's function against the arbitrary source distribution. This is a powerful concept as it transforms the problem of solving a differential equation into one of integration.

Green's functions are widely used in various fields, including quantum field theory, solid-state physics, electromagnetism, and the study of wave phenomena. They provide a systematic way to solve boundary value problems and understand the behavior of physical systems. The specific form of the Green's function depends on the differential operator and the boundary conditions of the problem. Determining the Green's function often involves techniques like Fourier transforms or solving integral equations.