Quantum Mechanics for Mathematics Students

Math 523 - Spring 2014

instructor phone # office e-mail
Renato Feres 5-6752 Cupples I, 17 feres@math.wustl.edu

Section information: Classes meet on Mondays, Wednesdays, Fridays, from 3:00PM to 4:00PM, on Cupples I room 216.

Subject: This is a course on the fundamentals of quantum theory for mathematics students. I do not assume any prior knowledge of quantum physics. On the math side, a good grounding in real analysis including some acquaintance with Lebesgue integration will be (more-or-less) taken for granted. Nevertheless, a good part of the course will consist of developing the analytical prerequisites, especially the general theory of operators on Hilbert spaces.

Text: I plan to use a variety of sources, but the basic plan corresponds to chapters 2 and part of 3 of Quantum Mechanics for Mathematicians by Leon A. Takhtajan (American Mathematical Society, Graduate Studies in Mathematics series, volume 95, 2008.) I may also take some material from Mathematical Foundations of Quantum Mechanics by K.R. Parthasarathy (Texts and Readings in Mathematics, volume 35, Hindustan Book Agency, 2005) in addition to some research papers I may bring up along the course. There are many good physics texts, of course, that contain all that I plan to do from a perspective perhaps more congenial to physics students. For the math students in class I recommend paying a visit to the physics library to see what is available. Concerning the general theory of Hilbert spaces my main source will be Linear Operators in Hilbert Spaces by Joachim Weidmann (Graduate Texts in Mathematics volume 68, Springer-Verlag, 1980.)

Tentative list of topics:

Coursework: A variety of exercises will be proposed throughout the course, although I will not collect them. At the end of the course students (only those who are enrolled) will give a presentation on a topic of their choice related to the subject of the course. I will be glad to propose themes if you like.