Symmetry of delta functions

Question

The above link has answers for the symmetry of the delta function as:

$V(x)=δ(x)$

If suppose I have a

$V(x)=λ(δ(x-ap)+δ(x-aq))$

And

$V(x)=λ(δ(x-a)+δ(x+a))$

I would guess the former is not even and the second is even. Can someone confirm it? Thanks in advance.

Whether the first is even or not depends on the values of $p$ and $q$. If $p+q=0$ then $V$ is even, otherwise not. — md2perpe, Aug 26 '19 at 17:15

Korra · Answer 1 · 2019-08-26T18:18:24.000

2

All should be even as delta function is even as

$δ(x)=δ(-x)$

Which implies,

$δ(x-a)=δ(-(x-a))$

And further,

$δ(x-a)+δ(x-b)=δ(-(x-a))+δ(-(x-b))$

The same can be shown using definition of delta functions as done in one of the answers for the above mentioned post in the question.

edited Aug 26 '19 at 18:18

answered Aug 26 '19 at 18:11

Korra

1 Answers1