I know that there are similar questions already answered here on Physics StackExchange but the following things are still unclear to me:
Is it correct that an electron inside a crystal with a band structure shown above can have any energy inside the band? What is this energy (neglecting such things as external magnetic fields etc.)?
How do I have to read these types of plots, i.e. where are the gaps? Or stated differently: How can I know from the picture which are the filled bands and which are the gaps? Is the region below the first line with an energy between -7 and -14 eV a band or a gap?
How comes that there are bands but if I consider only one atom this has a parabolic energy dispersion with only one allowed energy for every k-vector. I have seen the calculation for two atoms and how there appears a gap. But there the electrons still can have only two energies per k-vector and I can't really make the jump to the continous bands. Is this under the (justified) assumption that there are infinitely many atoms? Unfortunately, every textbook makes this jump directly without ever explaining it rigorously, i.e. with a calculation (altough it kind of makes sense).