MAT 570: Concepts of Quantum Mechanics
Spring 2009
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.
Schedule: MWF 11:45-12:40 pm, Physics P 122.
Instructor: Leon Takhtajan, Math Tower 5-111, Phone:
632-8287,
Office hours: TBA
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.
Textbook: L. Takhtajan Quantum Mechanics for Mathematicians Amer. Math. Soc. "Graduate Studies in
Mathematics" vol. 95, 2008; Additional Material and Errata.
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.
DSS advisory. If you have a physical, psychiatric,
medical, or learning disability that may affect your ability to carry out
the assigned course work, please contact the office of Disability Support
Services (DSS) at 632-6748/TDD or http://studentaffairs.stonybrook.edu/dss.
DSS will review your concerns and determine what accommodations may be
necessary and appropriate. All information and documentation of disability
is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their
needs with their professors and Disability Support Services. For procedures and information
go to the following website: http://sunysb.edu/ehs/fire/disabilities.shtml.