In mathematics, a Green's function (or Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with...

Multiscale Green's function (MSGF) is a generalized and extended version of the classical Green's function (GF) technique for solving mathematical equations...

"Unit 2-1-S: Supplementary Material – Green's Identities, Uniqueness, Dirichlet and Neumann Green's Functions" (PDF). PHY415: Electrodynamics (Fall 2020)...

therefore, often called (causal) Green's functions (called "causal" to distinguish it from the elliptic Laplacian Green's function). In non-relativistic quantum...

In physics, the Green's function (or fundamental solution) for the Laplacian (or Laplace operator) in three variables is used to describe the response...

Green function might refer to: Green's function of a differential operator Deligne–Lusztig theory (Green function) in the representation theory of finite...

\left(\Box +{\frac {m^{2}c^{2}}{\hbar ^{2}}}\right)\psi =0~.} The Green's function, G ( x ~ − x ~ ′ ) {\displaystyle G\left({\tilde {x}}-{\tilde {x}}'\right)}...

the Green's functions used to solve inhomogeneous differential equations, to which they are loosely related. (Specifically, only two-point "Green's functions"...

In mathematical heat conduction, the Green's function number is used to uniquely categorize certain fundamental solutions of the heat equation to make...

variable, the Green's function is a solution of the initial value problem (by Duhamel's principle, equivalent to the definition of Green's function as one with...

then Green's theorem follows immediately for the region D. We can prove (1) easily for regions of type I, and (2) for regions of type II. Green's theorem...

many-body effects, one can resort to so-called Green's function methods. Indeed, knowledge of the Green's function of a system provides both ground (the total...

modern Green's theorem, the idea of potential functions as currently used in physics, and the concept of what are now called Green's functions. Green was...

of pre-defined basis functions; generally, the coefficients of these basis functions are the sought unknowns. Green's functions and Galerkin method play...

diffusion quantum Monte Carlo is a quantum Monte Carlo method that uses a Green's function to calculate low-lying energies of a quantum many-body Hamiltonian...

and λ {\displaystyle \lambda } a complex number, the Green's function considered to be a function of v is the unique solution to ( H − λ ) G ( v , w ;...

the Green's function describes the influence at (x′, y′, z′) of the data f and g. For the case of the interior of a sphere of radius a, the Green's function...

same way as the fields, the Green's function can be decomposed into vector spherical harmonics. Dyadic Green's function of a free space a: G ^ 0 ( r...

linear response functions such as susceptibility, impulse response or impedance; see also transfer function. The concept of a Green's function or fundamental...

obtain Laplace's equation. Poisson's equation may be solved using a Green's function: φ ( r ) = − ∭ f ( r ′ ) 4 π | r − r ′ | d 3 r ′ , {\displaystyle \varphi...

interior of the solution domain. BEM is applicable to problems for which Green's functions can be calculated. These usually involve fields in linear homogeneous...

well-known methods for linear differential equations. The primary Green's function of Stokes flow is the Stokeslet, which is associated with a singular...

relate the Green's function in D {\displaystyle D} dimensions to the Green's function in D + n {\displaystyle D+n} dimensions. Given a function s ( t , x...

into a problem of constructing what we now call Green's functions, and argued that Green's function exists for any domain. His methods were not rigorous...

is the Green's function of this equation, that is, the solution to the inhomogeneous Helmholtz equation with f equaling the Dirac delta function, so G...

equations for Green's functions non-perturbatively, which generalize Dyson's equations to the Schwinger–Dyson equations for the Green functions of quantum...

and eigenvalues of L, and the Green's function corresponding to L can be found. Applying R to some arbitrary function in the space, say φ {\displaystyle...

{F}}(z)=(e^{\beta z}+1)^{-1}} is the Fermi–Dirac distribution function. In the application to Green's function calculation, g(z) always have the structure g ( z )...

In quantum field theory, correlation functions, often referred to as correlators or Green's functions, are vacuum expectation values of time-ordered products...

{r} ,\mathbf {r} ^{\prime })} is the three-dimensional homogeneous Green's function given by G ( r , r ′ ) = e − j k | r − r ′ | | r − r ′ | {\displaystyle...