Sumários

T10 - Tensores Irredutíveis

30 Novembro 2023, 11:00 • Ana Maria Formigal de Arriaga

Irreducible tensors

  • commutation relations of irreducible tensors with the angular momentum – continuation
  • examples of irreducible tensors
  • operations with irreducible tensors: sum and tensor product
  • examples of tensor product of irreducible tensors

TP9 - Série 4

23 Novembro 2023, 16:30 • Ana Maria Formigal de Arriaga

Série 4

Rotation operator

Suggestions, and discussion, for the resolution of problems : problem 1b)-e), 2 and 3a) e b)

T9 – Operador Rotação e Tensores Irredutíveis

23 Novembro 2023, 11:00 • Ana Maria Formigal de Arriaga

Rotation operator – with spin

  • commutation relations of the Hamiltonian with the angular momentum and the invariance under rotations
  • matrix representation of the rotation operator
    • rotation matrices in terms of the Euler angles
    • Wigner matrices
  • Recurrence relation

Irreducible tensors

  • transformation of observables under rotations
    • examples of scalars, observables invariant under rotation, tensors of rank 0
    • examples of vectors, tensors of rank 1
  • formal definition of irreducible tensors of rank k.
  • commutation relations of irreducible tensors with the angular momentum

TP8 - Séries 3 e 4

16 Novembro 2023, 16:30 • Ana Maria Formigal de Arriaga

Série 3

Interaction with magnetic fields and Coupling of Angular Momenta

Suggestions, and discussion, for the resolution of problems : problem 10-11

Série 4

Angular momentum operator

Suggestions, and discussion, for the resolution of problems : problem 1a)


T8 – Operador Rotação

16 Novembro 2023, 11:00 • Ana Maria Formigal de Arriaga

Rotation operator – no spin

parameters of the rotation.

rotation operator in R3 (coordinates space).

rotation operator in E (quantum states space).

rotation generators – cartesian components of the orbital angular momentum; commutation laws

Rotation operator – with spin

rotation operator in E (quantum states space).

rotation generators – cartesian components of the total angular momentum; commutation laws

consequences of the application of the rotation operator in an eigenstate of S2 and Sz.