3d year, spring term

1. Mathematical tools of quantum mechanics: Linear algebra, theory of linear space, theory of linear operators.

2. Mathematical tools of quantum mechanics: operations with operators. Finding eigenfunctions and eigenvalues of Hermitian and non-Hermitian operators. Functions from operators.

3. Mathematical tools of quantum mechanics: Operator function (continuation). Matrix-operators in space En. Properties of Pauli matrices.

4. Mathematical tools of quantum mechanics: Calculating expectation value of operators. Elements of representation theory. Discrete and continuous representations.

5. Mathematical tools of quantum mechanics: Momentum representation. One-dimensional (1D )movement: 1D free particle, 1D infinite square well.

6. 1D movement: One-dimensional movement in the piecewise continuous potentials. Discrete spectrum and continuous spectrum.

7. 1D movement: Movement in the piecewise continuous potentials. (continuation). Schrodinger’s equation in momentum representation. Transfer-matrix: calculating of transmission coefficient, energy spectrum of periodic potentials.

4th year, fall term

8-9. Refresher course of previous semester:main equations and concepts of quantum mechanics. New topic: Angular Momentum. Commutation relations. Eigenfunctions and eigenvalues of of the angular momentum z-projection and the squared angular momentum. "Ladder operators".

10. Central field: two-body problem in QM, plane rigid rotator, spacial rigid rotator.

11. Central field: spherical waves, spherically symmetrical rectangular well of finite depth.

12. Perturbation Theory (PT): time-independent PT.

13. Perturbation Theory (PT)): time-dependent PT.

14. Quasi-classical approximation: Bohr-Sommerfeld quantization rule.

15. Quasi-classical approximation: tunneling.

16. Spin-1/2.

17. Spin.(ending)