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At this point it is worth while to introduce the Dirac delta function. In one
dimension, the delta function, written d(x — a), is a mathematically improper
function having the properties : (1) d(x — a) = 0 for x =£ a, and (2) I 5(x — a) dx =
1 if the ...
From the definitions above it is evident that, for an arbitrary function /(#), (3) f /(a;)
d(x -a)dx = f(a), and (4) f /(*) <5'(* -a)dx = -f'(a), where a prime denotes
differentiation with respect to the argument. If the delta function has as argument
a function ...
... and d(r — r,-) is the radial delta function.* Under inversion the angular factor is
unchanged. Consequently we have The radial delta function can be transformed
according to rule 5 at the end of Section 1.2 as a* * r» / a*\ a\l a* \ -- r,.| = -2<5|r ...
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Introduction to Electrostatics
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