Dirac Delta Function
A generalized function (distribution) that is zero everywhere except at x = 0 where it is infinite, with an integral over all space equal to 1.
Governing formula
δ(x) = 0 for x ≠ 0, ∫_(-∞)^(∞) δ(x) dx = 1, ∫ f(x) δ(x - a) dx = f(a)
SI unit
1 / [x Unit]
In depth
Introduced by Paul Dirac. Serves as a mathematical idealization for localized point sources (point charge, point mass, instantaneous impulse). Acts as the identity operator in function space under sifting property.
Examples in the real world
Representing a point electric charge density ρ(r) = q δ(r - r₀) in electrodynamics.