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I am looking for a good mathematical rigorous introduction to solid state physics. 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.
Edit: 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:
This post has been migrated from (A51.SE)
The following books discuss rigorous methods in solid state physics:
See also the course by Rivasseau given
at the CIME school in Cetraro, September 2010.
You can wonder about the stability of matter in quantum mechanics or get caught by disorder to learn the rigorous aspects of localization in disordered systems.
The problem with this kind of books is that there is no special mathematics in solid state physics. There are books with titles like "Quantum Field Theory in Solid State Physics" or similar: modern methods in solid state originate from QFT, quantum chemistry and alike. Thus, rigorous introduction may be found there and not in solid state itself.
If you could specify particular topic, probably it would be possible answer your question.
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