T23 – Groups and Symmetries

28 Novembro 2024, 11:00 • Ana Maria Formigal de Arriaga

Groups and Symmetries

• Symmetries and laws of conservation
• Different categories of symmetries
• Definition of a group
• Isomorphic groups
• Representations of a group
• Matrix representation of a group
• Representation of a group in the Hilbert space of the wave functions and in the coordinates space

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T22 – Irreducible tensors and Groups and Symmetries

26 Novembro 2024, 11:00 • Ana Maria Formigal de Arriaga

Irreducible tensors

• Wigner-Eckart theorem: proof, second part, and examples

Groups and symmetries

• General considerations about the importance of symmetries in Physics

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TP10 - Rotations

21 Novembro 2024, 12:00 • Ana Maria Formigal de Arriaga

·         Suggestions for resolution of problems: 1b)-e), 2, 3 and 4

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T21 – Irreducible tensors

21 Novembro 2024, 11:00 • Ana Maria Formigal de Arriaga

Irreducible tensors

• operations with irreducible tensors: product
• examples of tensor product of irreducible tensors
• Wigner-Eckart theorem: proof , first part

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T20 – Irreducible tensors

19 Novembro 2024, 11:00 • Ana Maria Formigal de Arriaga

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
• examples of irreducible tensors
• operations with irreducible tensors: sum of tensors of the same rank

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