Do Different Quantum Numbers Allow Energy Bands to Overlap?

[abdullahbameh]

How Can Energy Band Over Lap?!

MY question is when i read energy band over lap i thought it is coming because of the huge number of atoms and the small distance between them but is it possible that energy bands of differnt energy bands get over lap and they are have different quantuam numbers?
and what does happen to the energy lap when it get over lapped with another energy band?

 

[zhanghe]

It is "Energy band" overlap not "Energy" overlap, so it is ok when the bands--which origin from different energy level from a single atom -- overlap,:). So, don't worry about the Pauly exclusion principle, these bands of energy levels will re-allocate the specific energys

 

[Timo]

Not exactly sure if I get the question, but I'll give it a try. Energy is not the only quantum number. Another -and closely related- quantum number is the wave vector (akin to momentum). If you take a look at the 2nd diagram on http://www.doitpoms.ac.uk/tlplib/semiconductors/images/bandsoverlappingnolabels.jpg
you'll see an example of what I think you meant by an energy band overlap (particle physicist here, so I am not familiar with the solid state physics terminology). As you can see, there is regions for the two bands that have the same energy, respectively. However, there is no point where any two points in the different curves had the same coordinates/quantum numbers (E,k). The Pauli principle only forbids double-occupation of states that are equal in all quantum numbers.