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Forums
Physics
Special and General Relativity
Relativistic Velocity Addition: Calculating Electron Speed
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[QUOTE="Sagittarius A-Star, post: 6643146, member: 666305"] The group velocity of the matter wave is equal to the velocity of the electron. As already mentioned by Orodruin, the relativistic velocity composition holds for any speeds. Accordingly, the "relativistic velocity addition" formula can be applied to both, the group velocity and the phase velocity. Source: [URL]http://www.scholarpedia.org/article/Special_relativity:_mechanics#Particles_and_Waves[/URL] Assume an electron moving in the unprimed frame with velocity ##u## in x-direction. You can transform it's velocity to a primed frame, which is moving with ##v## in x-direction, by applying the "relativistic velocity addition" formula: ##u' = u \oplus (-v) = \frac{u-v}{1-uv/c^2}## The phase velocity in the unprimed frame is ##w = \frac{c^2}{u}##. If you apply the "relativistic velocity addition" formula to this phase velocity, then you get: ##w' = w \oplus (-v) = \frac{(c^2/u)-v}{1-(c^2v/uc^2)} = \frac{1-uv/c^2}{(u/c^2)-(v/c^2)} = c^2/u'##, as it should be. [/QUOTE]
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Physics
Special and General Relativity
Relativistic Velocity Addition: Calculating Electron Speed
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