Through the superposition principle for linear operator problems, the convolution of a Green's function with an arbitrary function f (x) on that domain is the solution to the inhomogeneous differential equation for f (x). In other words, given a linear ordinary differential equation (ODE), L(solution) = source, one can first solve L(green) = δs, for each s, and realizing that, since the source is a sum of delta functions, the solution is a sum of Green's functions as well, by linearity of L.
Green's functions are named after the British mathematician George Green, who first developed the concept in the 1830s. In the modern study of linear partial differential equations, Green's functions are studied largely from the point of view of fundamental solutions instead.
Under many-body theory, the term is also used in physics, specifically in quantum field theory, aerodynamics, aeroacoustics, electrodynamics, seismology and statistical field theory, to refer to various types of correlation functions, even those that do not fit the mathematical definition. In quantum field theory, Green's functions take the roles of propagators.
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Historically the debye was defined as the dipole moment resulting from two charges of opposite sign but an equal magnitude of 10−10 statcoulomb (generally called e.s.u. This gave a convenient unit for molecular dipole moments.)
The Grüneisen parameter, γ, named after Eduard Grüneisen, describes the effect that changing the volume of a crystal lattice has on its vibrational properties, and, as a consequence, the effect that changing temperature has on the size or dynamics of the lattice. The term is usually reserved to describe the single thermodynamic property γ, which is a weighted average of the many separate parameters γi entering the original Grüneisen's formulation in terms of the phonon nonlinearities.
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The relative permittivity of a material is its (absolute) permittivity expressed as a ratio relative to the permittivity of vacuum.
Permittivity is a material property that affects the Coulomb force between two point charges in the material. Relative permittivity is the factor by which the electric field between the charges is decreased relative to vacuum.
Likewise, relative permittivity is the ratio of the capacitance of a capacitor using that material as a dielectric, compared with a similar capacitor that has vacuum as its dielectric. Relative permittivity is also commonly known as dielectric constant, a term deprecated in physics and engineering as well as in chemistry.
The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI units for electric dipole moment are coulomb-meter (C.m); however, the most common unit is the debye (D).
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