The de Broglie formula is normally given as: $\lambda=h/mv$. Does this hold for velocity near the speed of light? In this case would you use the rest mass or relativistic mass?
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The de Broglie wavelenght comes from assuming massive particles have the same relations as the photon:
$$ E=\frac{hc}{\lambda}=pc, $$
so that $$ \lambda_B =\frac{h}{p}=\frac{h}{\gamma mv}=\frac{h}{mv}\sqrt{1-\frac{v^2}{c^2}}, $$
which reduces to the usual $\frac{h}{mv}$ in the non-relativistic limit ($c\to\infty$).
