Often used in conjunction with Green's function, which determines the impulse response of a differential equation, this function is sometimes known as the unit impulse function.  
Among its properties are the sifting property and the integral property, which defines the Heaviside unit step function.  Often used in conjunction with Green's function, which determines the impulse response of a differential equation, this function is sometimes known as the unit impulse function.  Created by its namesake to deal with the completeness relation for position and momentum eigenstates, FTP, identify this equation of quantum mechanics that deals with the action of heat flow over a very small region and named after the scientist that predicted antimatter.
Among its properties are the sifting property and the integral property, which defines the Heaviside unit step function.  
Dirac delta function