# Simplification - complicated summation involving delta functions

1. Apr 2, 2014

### Halaaku

Simplification -- complicated summation involving delta functions

1. The problem statement, all variables and given/known data

$\frac{1}{\sqrt{(2^3)}}$$\sum[δ(k+1)+δ(k-1)]$|k> for k=0 to 7

2. Relevant equations

3. The attempt at a solution
I am trying to simplify the above expression. I get $\frac{1}{∏*\sqrt{(2^3)}}$ |1>, which is incorrect because |1> should have occurred with a constant 1.
Is it right to say that the first delta function can be ignored because my K is not defined for -1?

2. Apr 3, 2014

### BvU

Is this really the correct problem statement ? Or just some step in a sequence of steps where you stumble at this point ?

Any idea what the |k> stand for ?

What definition of (or prescription for) $\delta$ do you have available under 2. ?

3. Apr 3, 2014

### Fredrik

Staff Emeritus
Halaaku, when you post in the homework forum, you need to state the problem more accurately than this, and then show us your thoughts on how to solve it.

If it's a sum rather than an integral, I have to assume that the deltas are Kronecker deltas rather than Dirac deltas. But if you use the notation $\delta(k-1)$ rather than $\delta_{k,1}$, I have to assume that these are Dirac deltas. The problem doesn't make much sense as it appears in your post.