A How many bands does a solid have?

[howl]

Usually, we only talk about the band near Fermi surface, but we know that atom could have infinite levels, so, for a solid, does it have infinite levels too? So, if we only talk about the levels near Fermi surface, are the eigenwavefunctions complete?

 

[ZapperZ]

Usually, we only talk about the band near Fermi surface, but we know that atom could have infinite levels, so, for a solid, does it have infinite levels too? So, if we only talk about the levels near Fermi surface, are the eigenwavefunctions complete?

I'm not sure what you mean by your question on whether "... the eigenwavefunctions complete". ALL wavefunctions in solids are approximate, because you are dealing with a lot of atoms here.

In any case, I do not know if you are aware of the band structure of solids. For example, are you familiar with the band structure shown in the figures in this link?

http://what-when-how.com/electronic...stals-fundamentals-of-electron-theory-part-3/

Each of those lines are the bands (E vs. k) in a particular solid. The simplified band diagram that most people are familiar with are the ones where the momentum (k) has been integrated out, leaving only the energy values E.

Zz.

 

[howl]

I'm not sure what you mean by your question on whether "... the eigenwavefunctions complete". ALL wavefunctions in solids are approximate, because you are dealing with a lot of atoms here.

In any case, I do not know if you are aware of the band structure of solids. For example, are you familiar with the band structure shown in the figures in this link?

http://what-when-how.com/electronic...stals-fundamentals-of-electron-theory-part-3/

Each of those lines are the bands (E vs. k) in a particular solid. The simplified band diagram that most people are familiar with are the ones where the momentum (k) has been integrated out, leaving only the energy values E.

Zz.

In your link, there are some bands, for instance,Si. The electrons occupy the lowest bands under Fermi surface. For example, the band marked Gamma25', while Gamma15 and Gamma2' are empty. In QM, we should use up all eigenstates to build up a complete basis, then , if we only use Gamma25', could we build a complete basis?

 

[ZapperZ]

In your link, there are some bands, for instance,Si. The electrons occupy the lowest bands under Fermi surface. For example, the band marked Gamma25', while Gamma15 and Gamma2' are empty. In QM, we should use up all eigenstates to build up a complete basis, then , if we only use Gamma25', could we build a complete basis?

I am very puzzled by this post.

Those lines represent the dispersion curve for each band. They are not "eigenstates", or basis functions.

I need to take a few steps back. When you do a tight-binding approximation, you take into account as many "neighbors" that you need to come up with an accurate enough band structure. You end up with the dispersion curve similar to what you see in those figures. Do you know of this?

Zz.

 

[DrDu]

You are right, in principle, there are infinitely many bands in a solid, however, most of them are unoccupied.

 

[DrDu]

In QM, we should use up all eigenstates to build up a complete basis, then , if we only use Gamma25', could we build a complete basis?

Of course not.