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https://texercises.com/exercise/phase-and-group-velocity-1/
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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
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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
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Branches
quantum physics, special relativity
Tags
group velocity, matter wave, phase velocity
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Difficulty
(2, default)
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0 (default)
Language
ENG (English)
Type
Algebraic
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