Dirac Delta Function: Application & Uses

[koustov]

how do we apply dirac delta function?when do we apply?

 

[HallsofIvy]

The "dirac delta function" is not a true function- it is a "distribution" or "generalized function". If you google "generalized function" you might find more information (I do not recommend using "distribution". Too many things are called "distributions".)

Most often the dirac delta function is used to represent a "point disturbance". For example if you tap a drum head at a single point or pluck a guitar string at a single point, you can represent that with a delta function. In quantum physics, you would use a dirac delta function to represent a particle for which you know a precise position (and so have no information about momentum). More generally, any function can be repsrented as an infinite sum of delta functions, representing the value of the function at each point.

 

[koustov]

suppose i want to calculate the electrostatic field of a charge at r=0...how do we apply dirac delta function along with nabla operator?