Search results
Results from the WOW.Com Content Network
In such cases, the solution provided by the use of the retarded Green's function depends only on the past sources and is causal whereas the solution provided by the use of the advanced Green's function depends only on the future sources and is acausal. In these problems, it is often the case that the causal solution is the physically important one.
In many-body theory, the term Green's function (or Green function) is sometimes used interchangeably with correlation function, but refers specifically to correlators of field operators or creation and annihilation operators. The name comes from the Green's functions used to solve inhomogeneous differential equations, to which they are loosely ...
Green's functions can be expanded in terms of the basis elements (harmonic functions) which are determined using the separable coordinate systems for the linear partial differential equation. There are many expansions in terms of special functions for the Green's function. In the case of a boundary put at infinity with the boundary condition ...
See Green's functions for the Laplacian or [2] for a detailed argument, with an alternative. It can be further verified that the above identity also applies when ψ is a solution to the Helmholtz equation or wave equation and G is the appropriate Green's function.
The Green's function number specifies the coordinate system and the type of boundary conditions that a Green's function satisfies. The Green's function number has two parts, a letter designation followed by a number designation. The letter(s) designate the coordinate system, while the numbers designate the type of boundary conditions that are ...
The function K(x,y) is variously known as a Green's function, or the kernel of an integral. It is sometimes called the nucleus of the integral, whence the term nuclear operator arises. In the general theory, x and y may be points on any manifold ; the real number line or m -dimensional Euclidean space in the simplest cases.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
In this example, the applied force is the probe and the stretching of the spring is its response to the probe. If the measured values of the Green’s functions of a solid are available, it will accurately characterize the response of a solid for engineering applications. For this reason, the Green’s function is also called the response function.