Série 6 - Grupos e simetrias

14 Dezembro 2023, 16:30 • Ana Maria Formigal de Arriaga

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Suggestions and discussion for the resolution of problems: problems 3-7

T11 – Grupos e simetrias

14 Dezembro 2023, 11:00 • Ana Maria Formigal de Arriaga

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Lie groups

• generators and the transformation properties of a set of states and of operators
• Casimir operators
• symmetry groups of the Hamiltonian

Rotations group

TP12 - Série 5 e 6

7 Dezembro 2023, 16:30 • Ana Maria Formigal de Arriaga

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Série 5

Suggestions and discussion for the resolution of problems: problems 4 and 5

Série 6

Suggestions and discussion for the resolution of problems: problems 1 and 2

T12 - grupos e simetrias

7 Dezembro 2023, 11:00 • Ana Maria Formigal de Arriaga

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Groups and symmetries

• Invariant subspaces and irreducible representations of a group
• Irreducible matrix representations of a group
• Set of states that transform as an irreducible representation of a group
• Set of operators that transform as an irreducible representation of a group
• Equivalent representations
• Maschke Theorem
• Non-equivalent irreducible representations
• Tensor product of equivalent representations
• Lie groups
• definition, representations, and generators
• commutation relations of the generators and structure constants of the group
• three important theorems on Lie groups

T10 - Série 4

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

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Rotation operator

Suggestions and discussion for the resolution of problems : problems 4c) e d) and 5-7