Ashcroft and Mermin's chapter 3, difficulties....

[MathematicalPhysicist]

Can any expert tell me have we overcome some/most of the difficulties described in chapter 3 of Ashcroft and Mermin in the Free Electron Model since the textbook was written?

In the cases that we have, what exactly did solve the difficulties described in this chapter?

If you want me I can copy paste the details from the book, in case you don't have a copy.

 

[no-ir]

Can any expert tell me have we overcome some/most of the difficulties described in chapter 3 of Ashcroft and Mermin in the Free Electron Model since the textbook was written?

In the cases that we have, what exactly did solve the difficulties described in this chapter?

If you want me I can copy paste the details from the book, in case you don't have a copy.

After the list of problems of the free electron gas picture in Chapter 3 you have the section entitled "Review of basic assumptions" where the authors list the assumptions that produced these problems: that the ions are treated as only maintaining charge neutrality and nothing else (the effects of a lattice and it's dynamics are simply ignored), that the electrons do not interact with one another (this is solved by Fermi liquid theory), and that we assume the relaxation-time approximation is always valid. After this is a list of chapter references, with short explanations, where these problems are solved by a more careful analysis. From my brief look at the list these problems were not meant as gaps in our knowledge at the time the book was written, but as motivational problems meant to get you interested enough to read the rest of the book, where these problems are all addressed and solved. Condensed matter systems are much more than free electron gases after all - if they weren't, condensed matter physics would really be a dead and boring subject, while it is anything but. :) Study on an all shall become clear. ;)

 

[MathematicalPhysicist]

Yes, I kept on reading and noticed what you said that it's a preface of the other chapters.

Nevertheless I would like to know what are the current open problem in Condensed Matter Physics.
I found someone else asking this same question at researchgate:
https://www.researchgate.net/post/Unsolved_problems_in_condensed_matter_physics

if you have more open problems, do tell.