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Green's functions are also useful tools in solving wave equations and diffusion equations. In quantum mechanics, Green's function of the Hamiltonian is a key concept with important links to the concept of density of states. The Green's function as used in physics is usually defined with the opposite sign, instead.
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 ...
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 ...
Multiscale Green's function (MSGF) is a generalized and extended version of the classical Green's function (GF) technique [1] for solving mathematical equations. The main application of the MSGF technique is in modeling of nanomaterials. [2] These materials are very small – of the size of few nanometers.
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 ...
For the imaginary time Schrödinger equation, instead, we propagate forward in time using a convolution integral with a special function called a Green's function. So we get (, +) = (, ′,) (′,) ′. Similarly to classical mechanics, we can only propagate for small slices of time; otherwise the Green's function is inaccurate.
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In quantum field theory, correlation functions, often referred to as correlators or Green's functions, are vacuum expectation values of time-ordered products of field operators. They are a key object of study in quantum field theory where they can be used to calculate various observables such as S-matrix elements.