I often see pictures like this in physics, this one for Silicon band structure.
(source, NB: it's the German page for Silicon).
There you see the plot of the energy in terms of the momentum $k$. Now, the problem is that we generally assume that we have periodic boundary conditions in a crystal, which means that $k$ is a discrete quantity.
On the other hand, in these drawings we always seem to have continuous values of $k$.
Now, either this is due to some problems in resolving the discreteness of $k$ in these plots or the theoretical idea of periodic boundary conditions is wrong.
Could anybody comment on this issue?