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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.
An analogy: When we say "the Adam's apple", we refer to a particular instance of the protuberance in the human neck, rather than a specific entity belonging to a person named Adam. Just like "the Green's function" refers to a specific Green's function in a given context, "the Adam's apple" refers to the particular Adam's apple of a given ...
There are some review article about applications of the Schwinger–Dyson equations with applications to special field of physics. For applications to Quantum Chromodynamics there are R. Alkofer and L. v.Smekal (2001). "On the infrared behaviour of QCD Green's functions". Phys. Rep. 353 (5– 6): 281. arXiv: hep-ph/0007355. Bibcode:2001PhR ...
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Similarly to classical mechanics, we can only propagate for small slices of time; otherwise the Green's function is inaccurate. As the number of particles increases, the dimensionality of the integral increases as well, since we have to integrate over all coordinates of all particles. We can do these integrals by Monte Carlo integration.