The dispersion relation for the free relativisitic electron wave is [tex] \omega (k) = \sqrt{c^2 k^2 + (m_e c^2/ \hbar)^2}[/tex]. Obtain expressions for the phase velocity and group velocity of these waves and show that their product is a constant, independent of k. From your result, what can you conclude about the group velocity if the phase velocity is greater than the speed of light?(adsbygoogle = window.adsbygoogle || []).push({});

The group velocity will be easy to find because I can just differentiate with respect to k. I am not really sure what to do for the phase velocity. I figure that since [tex]v_p = f \lambda = E/p [/tex] then I could use the relativistic energy expression [tex]E = (p^2 c^2 + m^2 c^4)^{\frac{1}{2}}[/tex]. I am unsure about how to tackle the momentum. Does an electron have a de Broglie wave dispersion?

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# Relativistic Electron Wave

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