Sumários

External magnetic field

30 Novembro 2022, 09:00 • Luís Bento

Relativistic corrections on the hydrogen atom Hamiltonean and energy states. External magnetic field, Zeeman and Paschen-Back effects. Aplication of the projection theorem to the magnetic dipole moment and angular momentum operators. 

Exercises - Projection theorem

25 Novembro 2022, 11:00 • Luís Bento

Resolution and presentation of exercises of series 2 by students.

Application of Wigner-Eckart theorem to scalar and vector operators including angular momentum. Projection theorem. 

Irreducible tensor operators

23 Novembro 2022, 09:00 • Luís Bento

General irreducible tensor operators. Products of irreducible tensors and action of tensor operators on angular momentum eigenstates. Second order tensor operators and associated irreducible tensors of order 0,1,2. Example: tensor product of vector operators. Electric quadrupole moment and its irreducible tensor components, relation with spherical harmonic functions.

Demonstration of Wigner-Eckart theorem. Application with electric quadrupole moment.

Irreducible tensor operators

18 Novembro 2022, 11:00 • Luís Bento

Properties of vector operators. Spherical components, commutation relations with angular momentum operators. Relation between position vector, electric dipole moment and spherical harmonic functions.

Equivalence between spin 1/2 and complex conjugate representation. Exercise 9 of Series 3.

Tensors

16 Novembro 2022, 09:00 • Luís Bento

Second order 3x3 tensors in Cartesian and polarization basis. Determination of eigentensors of total spin 0,1,2 in both basis. Application to gravitational waves. Addition of spherical harmonic functions.