Quantum Mechanics: Basic Principles and Probabilistic Methods
Here is the
official
site from the department.
Time and place: Tuesday 12 in MS.05, Thursday 910 in B3.03, and Friday 23 in B3.02.
Support classes: Monday 121 in B3.01, by
Benjamin Lees.
Assessment: 3hour examination.
Description:
Quantum mechanics is one of the most successful scientific theories. It describes systems on the atomic scale and its development
is a key step in the ongoing electronic revolution.
This lecture will start with a brief introduction to the fundamental principles of quantum theory:
Origins; wave functions in Hilbert space; stationary and timedependent Schrödinger equations,
uncertainty principle.
Then we will take a quantum leap and discuss quantum spin systems, that are key to our understanding
of condensed matter physics. Specifically, we will review spin operators; tensor products of Hilbert
spaces; Heisenberg models; infinitevolume systems; phase transitions; graphical representations of
quantum spin systems.
Mathematically, there will be some analysis, PDEs, Fourier analysis, functional analysis, algebra, and probability theory.
But no prerequisites beyond 2nd year core modules will be assumed; this lecture will be selfcontained.
Lecture notes:
References:

V. Betz,
2012 lecture notes, unpublished

W.G. Faris,
Outline of Quantum Mechanics, in Entropy and the Quantum, Contemp. Math. 529, 152 (2010)

J. Fröhlich, B. Schubnel,
Do we understand quantum mechanics  finally?, 2012.

S.J. Gustafson, I.M. Sigal,
Mathematical concepts of quantum mechanics, Springer, 2003.

A. Messiah,
Quantum mechanics, Dover, 1999.