After successful completion of the course, students are able to know the mathematical apparatus of the quantum theory of angular momentum and to apply it to experiment-related problems of spectroscopy. 

1. Rotation group and its irreducible representations.  Spherical harmonics; spin functions.  Wigner D-functions for rotations.   2. Addition of quantum angular momenta.  Clebsch-Gordan coefficients and the algorithm of their calculation.  3j-symbols and their symmetries. Sums involving 3j-symbols. Irreducible tensors.    3. Further adding of angular momenta: 6j-symbols and their symmetries.  Sums involving 6j-symbols.    4. The Wigner-Eckart theorem.  Calculation of matrix elements of practically important operators.    5. Adding several identical spins.  Permutation symmetry of the co-ordinate part of the wave function of a multi-particle  system and the allowed values of the total spin.     6. Application of the quantum angular momentum theory in atomic and molecular  physics (branching ratios for the channels of radiative decay of excited states;  statistical weights of states; hyperfine splitting and the Zeeman effect; ac Stark shift). 

From the methodical point of view, this course follows the theoretical approach by D. A. Varshalovich, A. N.  Moskalev, V. K. Khersonskii, "Quantum Theory of Angular Momentum" (World Scientific, Singapore, 1988). The derivation of the formalae and the example calculations will be demonstrated in detail. 

Discussion of a scientific paper, where the application of the quantum theory of angular momentum plays an important role. 

Physics III; linear algebra