Dirac Delta (Electrodynamics)

1. Oct 18, 2009

E&M

1. The problem statement, all variables and given/known data

I am really confused in my electrodynamics class. I have the following function.

f(x) = $$\delta$$ (x + $$\alpha$$ ) + $$\delta$$(x -$$\alpha$$)

How do i convert this into Fourier Tranform ?
Those are dirac delta functions on either sides of the origin.

2. Relevant equations

no clue

3. The attempt at a solution

I multiplied f(x) by 1/sqrt(2*pi)*e-ikt and integrated the whole thing.

2. Oct 18, 2009

Donaldos

And what did you get?

3. Oct 18, 2009

E&M

1/$$\sqrt{2\pi}$$$$\int$$$$\delta$$(x+$$\alpha$$)e-ikx + $$\delta$$(x-$$\alpha$$)e-ikx dx

I tried to integrate those terms by parts (uv substitution).

$$\int$$$$\delta$$(x+$$\alpha$$) = 1. Isn't that right ?
Also I think f(x)$$\int$$$$\delta$$(x+$$\alpha$$) = f($$\alpha$$). Am i right ?

4. Oct 18, 2009

Donaldos

All you need is the following property:

$$\int\limits_{-\infty}^{+\infty} f(x)\delta\left(x-a\right)=f(a)$$

5. Oct 18, 2009

E&M

so

$$\int$$e-ikx $$\delta$$ (x - a) = e-ika ?

6. Oct 18, 2009

Exactly.