Course and unique no.: M393C (54705)
Instructor: Hans Koch Time and Place: TTH 11:00-12:30 RLM 6.112
Brief description:
Quantum mechanics is the theory of atomic and subatomic phenomena.
Its mathematical framework is the theory of linear operators on Hilbert space.
Both play an important role in modern science an technology.
This introductory course covers the basic concepts of quantum mechanics
and develops the relevant mathematical tools.
Other important phenomena will be covered at a more formal level,
with references to the relevant literature.
The lectures will be aimed
at a diverse audience of graduate students in science and mathematics.
The topics that we will try to cover are:
1. Preliminaries:
from classical to quantum mechanics,
the Schrödinger equation,
exactly solvable cases.
2. Linear Operators:
Hilbert spaces,
projections,
self-adjoint and unitary operators,
Fourier transform,
spectral theorem,
relative compactness.
3. Eigenstates:
perturbation theory,
variational methods,
number of eigenstates,
harmonic oscillator,
hydrogen atom.
4. Time Evolution:
time dependent scattering theory,
perturbation theory,
(semi)classical limit,
examples.
5. Quantum Fields:
second quantization,
Poincaré group,
spin and statistics,
path integrals,
Feynman-Kac formula,
perturbation theory.
Prerequisites: Undergraduate analysis and linear algebra will be useful.
Textbook(s):
None.
A list of references will be posted on the
web
by the end of August.
Consent of instructor required: No