Kronecker Delta

1. Apr 19, 2007

theperthvan

the Kronecker Delta function is
What does it mean when the subscript is not i,j but i+j?

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2. Apr 19, 2007

MathematicalPhysicist

where did you see this with i+j?

3. Apr 19, 2007

theperthvan

It was in an assignment.
I wanted to post the whole question but have no idea how to use latex that well (only basic).
If you can get this, it was:
Show that:
Integrate[e^(ix(m+n)),{x,0,2pi}] = 2pi*delta(m+n)

the LHS should vaguely resemble a Mathematica input and the RHS (m+n) should be subscript.
I thought it might be a mistake in his notes but in the lecture he made no correction.
We haven't learnt this function, but this is a 2nd year course on Mathematical Methods and the lecturer is in love with Mathematica. If it were a person I reckon he would marry it. so knowledge of the function wasn't rea;;y necessary.

4. Apr 19, 2007

Moo Of Doom

In this case, it means 1 when (m+n) = 0 and 0 otherwise.

5. Apr 19, 2007

HallsofIvy

Staff Emeritus
Integrate[e^(ix(m+n)),{x,0,2pi}] = 2pi*delta(m+n)
$$\int_0^{2\pi} e^{ix(m+n)} dx= 2\pi \delta_{m+n}$$
(click on the equation to see the code)

If m+n is not 0, then the integral is
$$-\frac{i}{m+n}e^{ix(m+n)}$$
evaluated from 0 to $2\pi$. But $e^{ix(m+n)}$ is 0 at both 0 and $2\pi$ so the integral is 0.

If m+n= 0 then the integral is
[tex]\int_0^{2\pi}dx= 2\pi[tex]

Yep, it looks like that "delta" should be "1 if m+n= 0, 0 otherwise".