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Dirac delta function

In a three-dimensional space the Dirac delta function:


has three properties:

The Dirac delta function can be utilized to describe a lattice.
Schematic representation of the Dirac delta function by a line surmounted by an arrow. The height of the arrow is usually used to specify the value of any multiplicative constant, which will give the area under the function.

The Dirac delta function as the limit (in the sense of distributions) of the sequence of Gaussians: