Relation between phase velocity and group velocity

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Discussion Overview

The discussion revolves around the mathematical relationship between phase velocity and group velocity in wave mechanics. Participants explore definitions and seek to clarify how these two concepts are interconnected, with a focus on deriving the relationship through calculation rather than external references.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • Some participants express familiarity with the definitions of phase and group velocity and seek a mathematical relationship between them.
  • One participant suggests that the group velocity might be the derivative of phase velocity, but expresses uncertainty about this claim.
  • Another participant clarifies that while group velocity can be related to the derivative of phase velocity with respect to wave number (k) or wavelength (λ), it is not simply equal to the derivative and raises concerns about dimensional consistency.
  • Several participants indicate difficulty in finding a specific relationship through direct calculation, rather than relying on external sources.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the exact mathematical relationship between phase velocity and group velocity. There are competing views on how these concepts relate, and uncertainty remains regarding the correct formulation.

Contextual Notes

Participants mention the need for direct calculation to find the relationship, indicating potential limitations in their current understanding or available resources.

iVenky
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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.
 
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If you know the definitions, you can easily find a relationship.
 
nasu said:
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.
 
iVenky said:
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?
 
nasu said:
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.
 
iVenky said:
Could not find anything.
I did not mean to look it up but to find it by direct calculation.
 

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