AMATH 473/673/PHYS 454: Quantum Mechanics 2

Offered every fall term.

Brief description:

Applications of quantum mechanics are ubiquitous in modern technology, for example in semi-conductors and super-conductors, in solar panels and lasers. Further practical applications of quantum mechanics are being developed, from quantum chemistry and nanotechnology to quantum computing and quantum cryptography. Also on the level of pure discovery, significant progress is currently being made, for example, in the field of quantum cosmology.

The aim of AMATH 473/673, PHYS 454 is to provide a solid basis from which interested students can proceed to both applied and pure research topics in quantum theory. To this end, the course introduces the full mathematical structure which underlies quantum theory, in the abstract formulations by Heisenberg, Schroedinger and Dirac. Among other topics, the course covers the deep relationships between symmetries and conservation laws, spin and statistics, as well as Bell's paradox and decoherence. Various mathematical techniques, relating, for example, to Poisson brackets and Hilbert spaces, will be introduced as needed.

Recommended textbook:

• "Advanced Quantum Mechanics", Lecture notes to be distributed by the Instructor.
• There are numerous textbooks on quantum mechanics. Students may wish to purchase a copy of one of the following books:
  • M. LeBellac, "Quantum Physics", Cambridge (2006); or
  • L.E. Ballentine, "Quantum Mechanics: A Modern Developmnent", World Scientific (2001).
• A good general reference is: "Quantum Mechanics", by Albert Messiah, re-issued by Dover. It is good value for money at 1152 pages for approximately 35$ CAD.

Prerequisites:

AMATH 373 or PHYS 334; level at least 4A in Math or Science, or instructor consent.

* Students taking this course as a graduate course will do extra homework and submit a short project report.