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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TP9 - Coupling of Angular Momenta and Rotations

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

Set 3: Coupling of angulat momenta

Resolution of second part of 10a)

Suggestions for resolution of problems: 10b) and 11

Set 4: Rotation operator

Suggestions for resolution of problems: 1a)

 

 

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T19 – Rotation operator

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

Rotation operator – with spin

• matrix representation of the rotation operator
• rotation matrices in terms of the Euler angles
• Wigner matrices
• recurrence relation

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