Course Plan for QM I

1. Basic Physical and Mathematical Concepts of QM:
• The Stern-Gerlach experiment; modern application in spinor Bose-Einstein condensates of cold atoms.
  
• Quantum states and the Hilbert space; observables, operators, bases and matrices; commutation relations and uncertainty rules
• momentum and space translations; wavefunctions in position and momentum space
2. Quantum Dynamics: 
   
• Schrödinger and Heisenberg equations; 
  
• quantization of the harmonic oscillator and the creation/annihilation operators;
• Propagators and Feynman path integrals*
• Potentials and gauge transformations
3. Theory of Angular Momentum:
• Rotations and the J operator; commutation relations and the spectrum of the angular momentum; representations, spin and the SU(2) group; orbital angular momentum and the central potential; adding angular momenta and Clebbsch-Gordan coefficients; tensors and Wigner-Eckart theorem; general continuous symmetries -- groups, generators, commutation relations and representations*
  
• Density operators and mixed ensembles
  
• Bell's inequality
4. Symmetry in QM*
   

In case of a class that needs stronger coverage of basic subjects (or if time is too short for any other reason), the subjects marked with a* would be sacrificed.

Textbook

J. J. Sakurai, ``Modern Quantum Mechanics", Addison-Wesley, 1994. (required).

Supplementary texts:

1. E. Merzbacher, Quantum Mechanics --- more difficult problems 
2. L.D. Landau and E. M.  Lifshitz, Quantum Mechanics (non-relativistic theory) --- a standard
3. C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum Mechanics (2 volumes) --- very detailed (1500 pages) with lots of examples
   
4. Albert Messiah,   Quantum Mechanics.