Unconventional methods to derive group and phase velocity relation

[neelakash]

Is there any unconventional method to find out the relation between group velocity and phase velocity? know there is a method employing Fourier tarnsforms and another easier method as well

 

[Meir Achuz]

Phase and group velocities only have meaning using a Fourier transform.
w/k and dk/dw are in terms of Fourier variables.

 

[Fizik]

one thing to notice is that, for a group velocity to be meaningful, the wave packet has to be merely composed of wavenumber in a narrow range.

 

[Meir Achuz]

one thing to notice is that, for a group velocity to be meaningful, the wave packet has to be merely composed of wavenumber in a narrow range.

That is a very good point. The equation v_g=dk/dw comes from keeping only the first term of a Taylor expansion. Many of the papers claiming funny group velocities for light miss the point you mention.