Quantum theory of angular momentum

Aim of course
The aim of this course is to make students acquainted with the mathematical formalism of the quantum theory of angular momentum and its applications in atomic and molecular physics.

The knowledge of the basic quantum mechnics is a prerequisite.

Schedule: The Lecture takes place in Summer Semester 2019, for all course dates please visit TISS

Subject of course

  • 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).