I recently stumbled across a small peculiarity I don't understand:
According to de Broglie, the frequency of a matterwave can be written as $f=\frac{E}{h}$, and its wavelength as $\lambda = \frac{h}{p}$.
However, relativistically for a particle with matter the following formulae are valid: $E = \gamma m_{0} c^{2}$, and $p = \gamma m_{0}v$, where $m_{0}$ is the particle's rest mass.
So, with $v=\lambda f$ (with the particle's velocity v, unequal the speed of light!), using de Broglie we would end up with $E=v p$, which is clearly not valid when inserting the relativistic energy and momentum equations:
$v*p = \gamma m_{0} v^{2} \neq E = \gamma m_{0} c^{2}$.
Where am I mistaken?
