What Does Not Allowed in Quantum Theory Mean Regarding Band Gaps?

[PainterGuy]

Hi,

Could you please help me with the queries below?

Question 1:
Please have a look on the attachment, conduction_band2, or check the following link for better resolution http://imagizer.imageshack.us/a/img921/4356/vODcjh.jpg

It says, "Figure 1–7 shows energy diagrams for insulators, semiconductors, and conductors. The energy gap or band gap is the difference between two energy levels and is “not allowed” in quantum theory."

What does the part "is not allowed in quantum theory" really mean here? I don't think it means that in quantum theory band gap is not allowed. If it does mean this then why does the gap exist?

Question 2:
Please have a look on the attachment, conduction_band1, or check the following link for better resolution http://imagizer.imageshack.us/a/img924/8813/KsYTN0.jpg

What do these 'arches' mean? Are they really needed? Why would the author use this style?

Thank you for the help!

 

[ZapperZ]

Hi,

Could you please help me with the queries below?

Question 1:
Please have a look on the attachment, conduction_band2, or check the following link for better resolution http://imagizer.imageshack.us/a/img921/4356/vODcjh.jpg

It says, "Figure 1–7 shows energy diagrams for insulators, semiconductors, and conductors. The energy gap or band gap is the difference between two energy levels and is “not allowed” in quantum theory."

What does the part "is not allowed in quantum theory" really mean here? I don't think it means that in quantum theory band gap is not allowed. If it does mean this then why does the gap exist?

It means that there are no energy levels in that region. It is similar to the gap between energy levels in an atom where you have discrete energy levels. Here, you have energy BANDS, instead of levels, and there are gaps in the range of energy where no states exist.

It exists because of many reasons, including the periodic nature of the potential.

Question 2:

Please have a look on the attachment, conduction_band1, or check the following link for better resolution http://imagizer.imageshack.us/a/img924/8813/KsYTN0.jpg

What do these 'arches' mean? Are they really needed? Why would the author use this style?

View attachment 236104

Thank you for the help!

Those should not be looked at as "arches", but rather as "plunging potential". Draw the Coulombic potential well, for example. It is -∞ as r→0, and then it approaches 0 as r→∞. This is ONE of those "arches". Now, repeat that when you have many lattice ions at regular intervals. This is the potential that an electron in a solid "sees" due to the regular arrangement of the lattice ions potential as it goes through the solid.

Zz.