MAT 570: Concepts of Quantum Mechanics
Spring 2006
Department of Mathematics
Stony Brook University
The purpose of this course is to
introduce mathematics students to the basic concepts and methods of
quantum physics, including sypersymmetry and Feynman's path integral,
which
play a profound role in geometry, topology, and other areas of
mathematics. For the physics students, the course may serve as a
(rather simplified) "dictionary" between mathematical and physical
"languages". No prior knowledge of physics will be assumed for
mathematics students.
Suggested books:
- Quantum fields and strings: a course for
mathematicians. Vol. 1, 2.
Material from the Special Year on Quantum Field Theory held at the
Institute for Advanced Study, Princeton, NJ, 1996--1997 Eds P. Deligne, P. Etingof, D. Freed, L. Jeffrey, D. Kazhdan, J. Morgan, D. Morrison and E. Witten. 1999. American Mathematical Society, Providence, RI;
Institute for Advanced Study (IAS), Princeton, NJ.
-
Mackey, George W.The mathematical
foundations of quantum mechanics.
A lecture-note volume.
Reprint of the 1963 original. Mathematical
Physics Monograph Series. Benjamin/Cummings Publishing Co.,
Inc., Advanced Book Program, Reading, Mass., 1980
Schedule: TuTh 11:20-12:40 pm, Old Chem 134
Instructor: Leon Takhtajan, Math Tower 5-111, Phone:
632-8287,
Office hours: Tu and W 4-5 pm in 5-111 and by appointment.
email: leontak@math.sunysb.edu.
Topics covered:
- Mathematical methods of classical mechanics, including Lagrangian
and Hamiltonian formalisms, symmetries and conservation laws
- Mathematical foundation of quantum mechanics, including
Heisenberg, Schrodinger and holomorphic representations.
- Stone-von Neumann theorem, H. Weyl quantization and deformation quantization.
- Schrodinger equation, including harmonic oscillator and hydrogen atom.
Prerequisites: The basic core courses curriculum and the basics from
MAT 551, MAT 552, MAT 568, MAT 569. All necessary facts from the theory of operators
in Hilbert spaces can be found in the last three monographs for the list of suggested
books.
Americans
with Disabilities Act
If you have a physical, psychological, medical
or learning disability that
may impact your course work, please contact Disability Support
Services,
ECC (Educational Communications Center) Building, room 128, (631)
632-6748.
They will determine with you what accommodations are necessary and
appropriate. All information and documentation is confidential.
Students requiring emergency evacuation are encouraged to discuss their
needs with their professors and Disability Support Services. For
procedures
and information, go to the following web site:
http://www.www.ehs.stonybrook.edu/fire/disabilities.asp