Exercise
https://texercises.com/exercise/phase-and-group-velocity-1/
Question
Solution
Short
Video
\(\LaTeX\)
No explanation / solution video to this exercise has yet been created.

Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
Derive the expressions for phase and group velocity for the de Broglie wave associated with a relativistic particle.

Solution:
The phase velocity of a relativistic particle is v_p fracomegak frachbaromegahbar k fracEp fracgamma E_gamma m v fracm c^m v resultfracc^v The group velocity is v_g fractextrmdomegatextrmdk frachbarfractextrmdEtextrmdk frachbarfractextrmdtextrmdksqrtpc^+E_^ frachbarfractextrmdtextrmdksqrthbar k c^+E_^ frachbar^ k c^hbarsqrthbar k c^+E_^ frachbar kE c^ fracpE c^ With the expression for the phase velocity it follows v_g fracc^v_p fracc^fracc^v resultv
Meta Information
\(\LaTeX\)-Code
Exercise:
Derive the expressions for phase and group velocity for the de Broglie wave associated with a relativistic particle.

Solution:
The phase velocity of a relativistic particle is v_p fracomegak frachbaromegahbar k fracEp fracgamma E_gamma m v fracm c^m v resultfracc^v The group velocity is v_g fractextrmdomegatextrmdk frachbarfractextrmdEtextrmdk frachbarfractextrmdtextrmdksqrtpc^+E_^ frachbarfractextrmdtextrmdksqrthbar k c^+E_^ frachbar^ k c^hbarsqrthbar k c^+E_^ frachbar kE c^ fracpE c^ With the expression for the phase velocity it follows v_g fracc^v_p fracc^fracc^v resultv
Contained in these collections:

Attributes & Decorations
Branches
quantum physics, special relativity
Tags
group velocity, matter wave, phase velocity
Content image
Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration
File
Link