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Lets say we have an electron with known De Broglie wavelength $\lambda$. Can anyone justify or explain why we calculate its energy $E$ using 1st the De Broglie relation $\lambda = h/p$ to get momentum $p$ and 2nd using the invariant interval to calculate $E$:

\begin{align} p^2c^2 &= E^2 - {E_0}^2\\ E &= \sqrt{p^2c^2 + {E_0}^2} \end{align}

Why we are not alowed to do it like we do it for a photon:

\begin{align} E=h\nu = h\frac{c}{\lambda} \end{align}

These equations return different results.

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  • $\begingroup$ Because of Pauli exclusion principle. $\endgroup$ – Veeramohan Jul 25 '13 at 10:59
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Note that the equation $E=h\nu$ does not account for the energy equivalent of particle's mass. It assumes zero mass.

Photons has zero mass. You can actually substitute zero for $E_0$ so that $p^2c^2 = E^2$, and then apply de Broglie's relations so that $E = h\nu$.

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    $\begingroup$ False. see Matter waves $\endgroup$ – Trimok Jul 25 '13 at 12:02
  • $\begingroup$ Maybee it really has to do something with a fact that an electron has a mass... $\endgroup$ – 71GA Jul 25 '13 at 15:16

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