Energy travels at group velocity and not phase velocity?

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SUMMARY

Energy travels at group velocity rather than phase velocity, as established in the discussion. The group velocity is defined as the speed at which the envelope of a wave packet propagates, which is crucial for energy transfer. However, it is important to note that group velocity does not always equate to the speed of energy transfer in all contexts. A comprehensive proof can be found in the paper titled "General Theorems on the Equivalence of Group Velocity and Energy Transport," published in the Physical Review.

PREREQUISITES
  • Understanding of wave mechanics
  • Familiarity with group and phase velocity concepts
  • Basic knowledge of energy transfer in physics
  • Ability to interpret academic papers in physics
NEXT STEPS
  • Read the paper "General Theorems on the Equivalence of Group Velocity and Energy Transport"
  • Explore the Wikipedia page on group velocity for foundational knowledge
  • Investigate the implications of group velocity in different physical systems
  • Study the relationship between wave packets and energy transport
USEFUL FOR

Physicists, students of wave mechanics, and researchers interested in the dynamics of energy transfer in wave phenomena.

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How to prove that energy travels at group velocity and not phase velocity?
 
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Start here: http://en.wikipedia.org/wiki/Group_velocity

Note that the group velocity is not always the speed for energy transfer!

A general proof is given in this paper: http://journals.aps.org/archive/abstract/10.1103/PhysRev.105.1129
"General Theorems on the Equivalence of Group Velocity and Energy Transport"
 
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