Simplification - complicated summation involving delta functions

[Halaaku]

Simplification -- complicated summation involving delta functions

Homework Statement

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

Homework Equations

The Attempt at a Solution

I am trying to simplify the above expression. I get [itex]\frac{1}{∏*\sqrt{(2^3)}}[/itex] |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?

 

[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. ?

 

[Fredrik]

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.