Can electrons have energies between valence and conduction bands? When looking at pictures of direct band gaps from a crystal lettice I wondered if it really is impossible that electrons, even if its only for a short time, occupy the Energies between the band gaps ? Or is it just that these Energies between the two gaps arent solid energies ? Meaning that an electron have such an energy value but it would want to (and actually do) decrease or increase its energy until its in the valence or conduction band.

 A: This is similar to asking if an electron, in say a hydrogen atom, can occupy an energy level somewhere in between the $n=1$ and $n=2$ levels.
In this instance, and in the context of your question, the energies of electrons are quantized, and therefore can only possess allowed energies and will occupy only allowed energy levels in the conduction and valence band. So they are forbidden from entering a band gap (provided it is an ideal lattice with no impurities). Certainly, there is no possible states for them to occupy in the band gap to begin with, much like there is no possible state for our electron in the hydrogen atom to be "between $n=1$ and $n=2$". This is the essence of quantum mechanics.
The statement "even if its only for a short time" does not appear to make sense either, since there are no energy levels in the band gap that can be occupied to begin with.
A: Allowed energies in the valence and conduction bands are the eigenenergies of the Schrödinger equation for an electron in the crystal potential. The gap really means absence of states with the energies between the top of the valence and the bottom of the conduction band (although there are actually more gaps and bands than these ones). Electron, of course, could be in a superposition of valence and conduction orbitals, with an average energy somewhere in the gap.
