Confused by Notation: Need Help Understanding c!

[tigger88]

Homework Statement

I'm just confused by notation in this question, because the textbook I use has different notation than my course notes and now I'm just not sure what anything means.

Homework Equations

Group velocity x Phase velocity = c^2

The Attempt at a Solution

What is c in this case? Is it the speed of light, or some other velocity?
I know it's a really stupid question...

Ta for any help though.

 

[millitiz]

Well, I assume that it is the speed of light. But really, the equation is not true in general.
Yes, photons move at c in free space, so phase velocity is c in free space (but inside midiums, the speed would get lower.).
However, the group velocity, could actually be lower than c. even 0. Just for reference, this is called EIT.
So if it is someother speed, well, normally it would be denoted as v, instead of c. c is normally reserved for the speed of light, or constant.
I guess what the most important part of this equation is that group velocity and phase velocity are the same in most of the cases: so if it is light, then it is c^2; if it is something else, then it is v^2. It is kinda open interpretation.

 

[diazona]

According to Wikipedia it is indeed the speed of light. I've never seen that particular equation before myself, but the derivation on Wikipedia looks reasonable...