![]() ![]() ) but there is not yet an established theory. ![]() There are phenomenological theories (BCS theory, Ginzburg-Landau theory. Dynamical Theory of Crystal Lattices - M.A seminar designed for mathematicians: MSRI-LBNL 2016 Summer School on Electronic Structure Theory.Computational Quantum Chemistry: A primer by Eric Cances, Mireille Defranceschi, Werner Kutzelnigg, Claude Le Bris, Yvon Maday, part III, Handbook of Numerical Analysis, Vol.An introduction to First-Principles Simulations of Extended Systems by Fabio Finocchi, Jaceck Goniakowski, Xavier Gonze, Cesare Pisani.You will find many mathematical models to play with, like Thomas-Fermi theory, DFT, tight-binding, Hubbard. Engel.Īs to what is interesting now read this article. Geometric Crystallography: An Axiomatic Introduction to Crystallography by P.In the following a set of topics within solid state theory and some references for the most rigorous treatments I found are presented. Therefore, I think it is best to first read general books of solid state to find what problems exist and then pick the model you like the most. So, you will probably not find a single mathematical treatment of everything but several models scattered all around. Sometimes we need advanced math from the beginning though. ![]() The more details the more involved the mathematical model is so it increasingly requires more advanced math. There is always a balance of what we want to reproduce and how simple (and enlightening) the model is. Once we can explain the rough characteristics, then we include more and more details. Besides, we build models that we think can explain the observations with each model requiring a specific type of math. Phenomenological models are built that with time are set on a more rigorous formulation. The theoretical developments in condensed matter are, I think, to a large extent motivated by experimental It is not unusual that they take a decade (even several decades) to solve. What is true, however, is that many of these problems turn out to be very hard. By carefully selecting the most important questions and formulating them as well-defined mathematical problems, and then solving a good number of them, Lieb has demonstrated the quoted opinion to be erroneous on both counts. Mathematical form, this is less so in Condensed Matter Physics, where some say that rigor is "probably impossible and certainly unnecessary". While in related fields, such as Statistical Mechanics andĪtomic Physics, many key problems are readily formulated in unambiguous In an excerpt from the last reference we can read the following: Theory under a mathematical formulation, starting from a set of axioms and going on. The style and level for this solid state physics book should be comparable to Abraham Marsdens Foundations of mechanics or Arnols mechanics book for classical mechanics or to Thirrings Physics course for quantum mechanics.Įdit: As a reaction to Peter Shor's comment, I try to narrow the scope of the question a bit and give some more specific subareas of solid state physics I am in particular interested in:įirst off, I would like to point out that solid state physics is not like quantum mechanics or maybe QFT in that you can articulate (nearly) the whole I am looking for a good mathematical rigorous introduction to solid state physics. Answers containing only a reference to a book or paper will be removed! Explain the nature of the resource so that readers can decide which one is best suited for them rather than relying on the opinions of others. Please write substantial answers that detail the style, content, and prerequisites of the book, paper or other resource. Before answering, please see our policy on resource recommendation questions. ![]()
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