Delta Functions

The so-called Dirac delta function is defined by its properties:

• It is normalized: .

• It is zero everywhere but at . (This makes mathematicians very uncomfotable; they prefer to call a ``distribution'' rather than a ``function.'')

• (most important) .

It has a number of handy representations:

• Gaussian representation: .

• Lorentzian representation: .

• Kronecker representation (square ``hill''):

  

• Fourier Integral representation: .