# Prove the property of Dirac's Delta

by phy07
Tags: delta, dirac, property, prove
 P: 939 Let $$\lbrace x_i \rbrace$$be the zeroes of function f(x). Near the zeroes, you can write the function as $$f(x) = f'(x_i)(x-x_i) + O(x-x_i)^2.$$ As the Dirac delta is entirely localized at xi, 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