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Prove the property of Dirac's Delta

by phy07
Tags: delta, dirac, property, prove
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phy07
#1
Apr11-12, 04:41 PM
P: 5
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 ... )
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clamtrox
#2
Apr12-12, 07:25 AM
P: 939
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 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
phy07
#3
Apr12-12, 10:54 AM
P: 5
Ok. Thank you clamtrox.


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