This function is the Schwartz kernel of the identity operator. The quantum 
This function is the Schwartz kernel of the identity operator. The quantum mechanical system corresponding to it is solved by matching the solutions at the origin but not the derivatives. An operator acting on its Green's function will give this function and the inner product of the position bra x with the position ket y is equal to this function of x minus y. When it is attractive, that system has exactly one (*) bound state. Scattering off this function has a reflection probability equal to one over one plus the square of momentum times scattering length. This function is the derivative of the step function, and it may be considered as the limit of a Gaussian that gets narrower and taller. For 10 points, name this function, equal to one when integrated, which is infinity at the origin and zero everywhere else.
This function is the Schwartz kernel of the identity operator.
Dirac delta function [or Dirac delta distribution, for mathematicians]