Quantum Mechanics: Basic Principles and Probabilistic Methods
Here is the official
from the department.
Time and place:
Tuesday 1-2 in MS.05, Thursday 9-10 in B3.03, and Friday 2-3 in B3.02.
Monday 12-1 in B3.01, by Benjamin Lees
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 time-dependent Schrödinger equations,
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; infinite-volume 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 self-contained.
2012 lecture notes, unpublished
Outline of Quantum Mechanics, in Entropy and the Quantum, Contemp. Math. 529, 1-52 (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.
Quantum mechanics, Dover, 1999.