Weak periodic potential-degeneracy

[moj20062001]

Hi;

In chapter 9 of Solid state physics of Ashcroft&Mermin(Electrons in a weak periodic potential),
there is a General Approch to the Schrödinger Equation when the Potential is Weak.

i can't understand what is meant by the term DEGENERACY?
or what does "nearly degenerate free electron levels mean"?
how should we visuallize degenerate and non-degenerate energy levels?
what are the differences and how can we interpret them?

i'm totally confused.

Thank u All.

 

[Dreak]

I haven't read/don't know the book, but degenerate means that the wave functions have the same energy.

In a single atom, all the atoms are in different orbitals which have different energy values, so they are 'non-degenerate'. (link 1)

In a conduction material, however, the electrons are bounded in bands, bands who are a few eV thick (link2).
In theory, those bands are still discrete (which means every electron has a different energy), but the differences is so small (few μeV, compared to a band which is a few eV thick, we can call it a continuum (which means the electrons have the 'same' energy), which means they are non-degenerate: different electrons with same energy.

link 1: http://library.thinkquest.org/C006669/media/Chem/img/Series.gif
link 2: http://chemwiki.ucdavis.edu/@api/deki/files/7389/=chemwiki_picure_2.jpg

 

[moj20062001]

I haven't read/don't know the book, but degenerate means that the wave functions have the same energy.

In a single atom, all the atoms are in different orbitals which have different energy values, so they are 'non-degenerate'. (link 1)

In a conduction material, however, the electrons are bounded in bands, bands who are a few eV thick (link2).
In theory, those bands are still discrete (which means every electron has a different energy), but the differences is so small (few μeV, compared to a band which is a few eV thick, we can call it a continuum (which means the electrons have the 'same' energy), which means they are non-degenerate: different electrons with same energy.

link 1: http://library.thinkquest.org/C006669/media/Chem/img/Series.gif
link 2: http://chemwiki.ucdavis.edu/@api/deki/files/7389/=chemwiki_picure_2.jpg

thanks Dreak.
but i know the meaning of degeneracy in such cases as you mentioned.
the problem is some how confusing in this case,i can't visuallize something like what you have shown in the links.
as a matter of fact,i can't get what is the term degeneracy referring to...!
i can send u the book if you want!?

 

[Dreak]

thanks Dreak.
but i know the meaning of degeneracy in such cases as you mentioned.
the problem is some how confusing in this case,i can't visuallize something like what you have shown in the links.
as a matter of fact,i can't get what is the term degeneracy referring to...!
i can send u the book if you want!?

Ai, don't know what you mean then :)

Don't have time now to see the book, I got an exam tomorrow, subject: 'solid state physics' ;)

 

[moj20062001]

Ai, don't know what you mean then :)

Don't have time now to see the book, I got an exam tomorrow, subject: 'solid state physics' ;)

Good luck!
:)
what is the book then,that you are studying?!
;)