Green's functions

E569215
integral kernel mathematical concept tool for solving differential equations

Green's functions are mathematical tools used in physics and engineering to solve inhomogeneous differential equations and describe the propagation of fields or particles in space and time.

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Observed surface forms (1)

Surface form Occurrences
Green's function 0

Statements (51)

Predicate Object
instanceOf integral kernel ⓘ
mathematical concept ⓘ
tool for solving differential equations ⓘ
alsoCalled fundamental solution (in some contexts) ⓘ
definedBy L G(x,x') = δ(x − x') for operator L ⓘ
dependsOn boundary conditions ⓘ
geometry of the domain ⓘ
describes propagation of fields ⓘ
propagation of particles ⓘ
response to a point source ⓘ
hasType Euclidean Green's function ⓘ
Feynman Green's function ⓘ
advanced Green's function ⓘ
causal Green's function ⓘ
retarded Green's function ⓘ
time-ordered Green's function ⓘ
historicalDevelopment introduced in the 19th century by George Green ⓘ
namedAfter George Green NERFINISHED ⓘ
property linearity with respect to the source term ⓘ
symmetry under certain conditions (self-adjoint operators) ⓘ
relatedTo Dirac delta function ⓘ
boundary integral methods ⓘ
boundary value problems ⓘ
convolution ⓘ
initial value problems ⓘ
linear differential operators ⓘ
resolvent of an operator ⓘ
spectral theory ⓘ
solves inhomogeneous differential equations ⓘ
usedIn acoustics ⓘ
applied mathematics ⓘ
condensed matter physics ⓘ
elasticity theory ⓘ
electrodynamics ⓘ
engineering ⓘ
physics ⓘ
potential theory ⓘ
quantum field theory ⓘ
quantum mechanics ⓘ
signal processing ⓘ
statistical mechanics ⓘ
usedToCompute Green's operators ⓘ
propagators in quantum field theory ⓘ
response functions ⓘ
usedToConstruct integral representations of solutions ⓘ
solutions of linear inhomogeneous equations ⓘ
usedToSolve Helmholtz equation NERFINISHED ⓘ
Poisson's equation ⓘ
Schrödinger equation (linear cases) NERFINISHED ⓘ
diffusion equation ⓘ
wave equation ⓘ

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Peierls bracket → relatedTo → Green's functions ⓘ
Methods of Mathematical Physics → hasTopic → Green's functions ⓘ
"Partial Differential Equations" → covers → Green's functions ⓘ
subject surface form: Partial Differential Equations