Dirac Delta Function: What It Does & How to Evaluate It

[Philosophaie]

What does the Dirac Delta Function do?

$\delta^3(\vec{r})$

How do you evaluate it?

What are its values from -inf to +inf?

 

[Jorriss]

Did google yield no useful results?

 

[Philosophaie]

It did not explain the vector r

 

[DimReg]

The vector just means that it is a function of x, y, and z.

Beyond that, I would say that you should try a bit harder to learn about the delta function without just asking us to explain it. It is typically introduced in either a Quantum mechanics course or an Electromagnetism course. Griffiths text on both subjects gives a non rigorous intro to the delta function.

 

[The_Duck]

So are you familiar with the 1-dimensional Dirac delta function? If so, the 3-dimensional delta function is just the product of three 1-dimensional delta functions, one for each component of the vector $\vec{r}$:

$\delta^3(\vec{r}) = \delta(r_x)\delta(r_y)\delta(r_z)$