Relation between Group velocity and Phase velocity

AI Thread Summary
The discussion focuses on the relationship between group velocity and phase velocity, emphasizing that both concepts are defined through Fourier transforms. It highlights that group velocity is meaningful only when the wave packet consists of wavenumbers within a narrow range. The equation v_g=dk/dw is derived from the first term of a Taylor expansion, which is crucial for accurate interpretations. Additionally, it points out that many studies misinterpret group velocities, often overlooking this essential detail. Understanding these relationships is vital for accurate wave analysis in physics.
neelakash
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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
 
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Phase and group velocities only have meaning using a Fourier transform.
w/k and dk/dw are in terms of Fourier variables.
 
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.
 
Fizik said:
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.
 

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