Prove the property of Dirac's Delta

phy07

1. The problem statement, all variables and given/known data
How can i prove this property of Delta,



2. Relevant equations
This is my homework from John David Jackson's Classical Elektrodynamics book


3. The attempt at a solution
I can't an attempt. Some properties is proved at wiki and other web pages but didn't find this.

(http://en.wikipedia.org/wiki/Dirac_delta_function and ... )

clamtrox

Let [tex]\lbrace x_i \rbrace [/tex]be the zeroes of function f(x). Near the zeroes, you can write the function as [tex]f(x) = f'(x_i)(x-x_i) + O(x-x_i)^2. [/tex] As the Dirac delta is entirely localized at x_i, you can just drop all higher order terms and it's still exact. Then you can use the scaling property of delta function, http://en.wikipedia.org/wiki/Dirac_d...g_and_symmetry

phy07

Ok. Thank you clamtrox.