Relation between phase velocity and group velocity

[iVenky]

I know the physical meaning of phase as well as the group velocity.

I want to know the mathematical relationship between the phase velocity and group velocity.

Thanks a lot.

 

[nasu]

If you know the definitions, you can easily find a relationship.

 

[iVenky]

If you know the definitions, you can easily find a relationship.

It looks as if the group velocity is the derivative of phase velocity but I don't think I am correct.

What's the exact relationship?

Thanks a lot.

 

[nasu]

It looks as if the group velocity is the derivative of phase velocity but I don't think I am correct.

The group velocity can be related to the derivative of phase velocity (in respect to k or λ
). It is not just equal to the derivative, it won't even make sens dimensionally. What relationship did you find?

 

[iVenky]

The group velocity can be related to the derivative of phase velocity (in respect to k or λ
). It is not just equal to the derivative, it won't even make sens dimensionally. What relationship did you find?

Could not find anything.

 

[Point Conception]

see: www.mathpages.com/home/kmath210/kmath210.htm

 

[nasu]

Could not find anything.

I did not mean to look it up but to find it by direct calculation.