Understanding of crystal wave vector

[Urmi Roy]

Hi All,

From the Schrödinger wave equation, I kind of understand what a wave function and hence a wave vector is, so I understand what a wave vector of an electron wave is.
However while talking about crystals, there is also a 'crystal wave vector'. Is this a vector sum of wave vectors of individual electrons?
While finding density of states of electrons, why is the electron wave vector used instead of the crystal wave vector?

 

[Urmi Roy]

So I've read that crystal wave vector corresponds to the group velocity while the electron's individual wave vector corresponds to it's phase velocity. However I'm still not sure if that means that the crystal wave vector means that it's effectively a 'net' or a sum of the individual ones.

The basic problem is that the group velocity is defined as 'delta_omega/delta_k', so what does this mean intuitively?