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Lecture notes
By the start of the course you will here find lecture notes. They will be continuously updated during the course.
For a recent and solid textbook on the topic (though lacking some of the techniques introduced in the course which are even more recent), consult:Elliot H. Lieb and Robert Seiringer, The Stability of Matter in Quantum Mechanics, Cambridge University Press, 2010. [errata etc]¶
Other useful books:Michael Reed and Barry Simon, Methods of Modern Mathematical Physics, Volumes I - IV, 1972-2010 caGerald Teschl, Mathematical Methods in Quantum Mechanics - With Applications to Schrödinger Operators, Second Edition, AMS, 2014Walter Thirring, Classical Mathematical Physics, Third Edition, Springer, 2003Walter Thirring, Quantum Mathematical Physics, Second Edition, Springer, 2003¶