Wann und wo: Di 14 - 16, SR 404, Eckerstr. 1
Vorbesprechung: Do 13.07.2017, 14:00, SR 403, Eckerstrasse 1.
Um teilzunehmen, kommen Sie bitte in die Vorbesprechung des Seminares; eine
Teilnehmerliste wird nicht vorab ausliegen.
Topic:
Classical physics does not predict the behaviour of
atoms and molecules correctly. Indeed, classically,
Coulomb's law implies that the electron of the
hydrogen atom should orbit around the proton, and thus the electron
continuously radiates energy and causes the hydrogen atom
to collapse. This contradicts the observed stability of the hydrogen atom.
One of the major triumphs of quantum mechanics is its explanation for
the stability of atoms.
Mathematically, a classical mechanical system can be described
by a so-called symplectic manifold M called the state space,
and the observables are functions on M.
A quantum mechanical system,
on the other hand, is described by a Hilbert space,
and the observables are "operators" on this Hilbert space.
A process which roughly associates to a classical theory a
quantum theory is called "quantization". Ideally, one would like to
associate to each classical observable a quantum observable,
but it is impossible to achieve this: there are no go theorems.
In practice, one has to lower one's expectation so that a reasonable
quantization process can be constructed.
The goal of this seminar is to study one particular method of
quantization called geometric quantization. Position space
quantization, momentum space quantization and
holomorphic quantization are particular instances of
geometric quantization. In
geometric quantization, one constructs the Hilbert space
from the square integrable sections of a
so-called complex line bundle over M.
Within the seminar, we will motivate and introduce the mathematical notions
that are needed for geometric quantization, starting from Newtonian mechanics.
Background knowledge
from physics is helpful but is not required.
Literatur:
Die Links führen auf Webseiten, von denen aus dem
Universitätsnetz die jeweiligen Referenzen
zugänglich sind. Falls kein Link gesetzt ist, finden
Sie die Referenz in der Bibliothek des Mathematischen Institutes
Freiburg.
Vortragsprogamm: hier
Tutorium: Santosh Kandel
