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Abstract

These are the lecture notes for a course that I am teaching at Zhiyuan College of Shanghai Jiao
Tong University (available at www.youtube.com/derekkorg), though the first draft was created for a previous course I taught at the University of Erlangen-Nuremberg in Germany. It has been designed for students who have only had basic training on quantum mechanics, and hence, the course is suited
for people at all levels (say, from the end of the bachelor all the way into the PhD). The notes are
a work in progress, meaning that some proofs and many figures are still missing. However, I’ve
tried my best to write everything in such a way that a reader can follow naturally all arguments
and derivations even with these missing bits. Also a few chapters are left to add, including one
on mathematical methods to analyze the dynamics of open systems, and another introducing the plethora of current experimental platforms where the tools and ideas developed in these notes are being currently implemented.