Introduction to Quantum Mechanics:
Mathematics W4391 (fall 2012)
Monday and Wednesday 1:10-2:25pm
Mathematics 307
This course will be an introduction to the subject of quantum
mechanics, from a perspective emphasizing the role of
symmetry. Most of the standard material and examples from
conventional physics courses will be covered, but with much greater
attention to the mathematical ideas behind the standard formalism
and usual calculational techniques. No specific background in
physics will be assumed, although an elementary physics course of
some kind would be helpful. The mathematical prerequisites are
multi-variable calculus (as in Calculus IV), and Linear Algebra.
Tentative
Syllabus
Lecture Notes
Note: The lecture notes for the course have been turned
into a book, available here.
I've removed the old lecture notes and problem sets, since
better versions of this material are incorporated in the book.
Since the perspective of the course will be different than any of
the available textbooks, especially at the beginning, I plan to
produce some lecture notes, which will be available here.
There will also be copies of readings from various sources that
will be made available to supplement the lecture notes and the
course textbook.
Problem Sets
There will be problem sets due roughly every other week, a midterm
(October 17) and a final exam.
Textbooks
A standard physics textbook at the upper-undergraduate to beginning
graduate level should be available to consult for more details about
the physics and some of the calculations we will be studying.
A good choice for this is
Principles of Quantum Mechanics, by Ramamurti Shankar.
Springer, 1994.
which does a good job of carefully working out the details of many
calculations. Two good undergraduate-level texts are
A Modern Approach to Quantum
Mechanics, John S. Townsend, University Science Books,
2000.
Introduction to Quantum Mechanics,
David J. Griffiths, Prentice-Hall, 1995.
The book
Linearity, Symmetry and Prediction
in the Hydrogen Atom, Stephanie Singer, Springer, 2005.
covers some of the material we will cover, especially the hydrogen
atom spectrum calculation, from a point of view similar to the one
of this course. It is available free on SpringerLink from
Columbia addresses at this
URL. At this site one can also purchase a printed copy
of the book for $24.95
Several suggestions for standard physics textbooks that provide good
references for some of the topics we will be considering are:
Quantum Mechanics, Volume 1,
by Cohen-Tannoudji, Diu and Laloe. Wiley, 1978
The Feynman Lectures on Physics, Volume III, by
Richard Feynman. Addison-Wesley 1965.
Lectures on Quantum Mechanics,
Gordon Baym.
Quantum Mechanics, Volumes 1 and 2,
Albert Messiah.
Quantum Mechanics, Volume 1,
Kurt Gottfried.
Introduction to Quantum Mechanics,
David J. Griffiths.
Quantum Mechanics and the
Particles of Nature: an Outline for Mathematicians,
Sudbery. Cambridge 1986 (unfortunately out of print)
Some other books at various levels that students might find helpful:
More mathematical:
An Introduction to Quantum Theory,
by Keith Hannabuss. Oxford, 1997.
Quantum Mechanics for
Mathematicians, by Leon Takhtajan. AMS, 2008.
Lectures on Quantum Mechanics for
Mathematics Students, by L.D. Fadeev and O.A. Yakubovskii.
AMS, 2009.
Some more from the physics side, available via Springerlink:
Quantum
Mechanics, Franz Schwabl.
Lectures
on Quantum Mechanics, Jean-Louis Basdevant.
Quantum
Mechanics, Daniel Bes.
A classic:
The Theory of Groups and Quantum
Mechanics, Hermann Weyl.
Also emphasizing groups and representations, but covering mostly
different material:
Group theory and physics,
Shlomo Sternberg.
More advanced, from the point of view of analysis:
Mathematical
Methods in Quantum Mechanics, Gerald Teschl
Recommended sources on Lie groups, Lie algebras and representation
theoy:
Naive
Lie Theory, John Stillwell
Groups and Symmetries: From Finite
Groups to Lie Groups, Yvette Kossmann-Schwarzbach
An Elementary
Introduction to Groups and Representations, Brian C. Hall
Lie groups, Lie algebras and
representations, Brian C. Hall
Representation Theory,
Constantin Teleman
Online Resources
Lecture
notes for a course on Quantum Computation, John Preskill
(especially Chapters 1-3)