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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T18 – Rotation operator

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

• 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 S_z
• invariance under rotations and commutation relations of the Hamiltonian with the angular momentum; conservation of the angular momentum

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TP 8 - Coupling of Angular Momenta

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

Set 3

Coupling of Angular Momenta

• Reading CG coefficients from a table
• Resolution of problem: 10a)
• Suggestions for resolution of problems: 8 and 9

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T17 – Rotation operator

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

Transformed state and transformed coordinates under a rotation

Parameters of the rotation.

Rotation operator in R₃ (coordinates space).

Rotation operator in E (quantum states space)

• for infinitesimal rotations about the z-axis
• for finite rotations about the z-axis
• for finite rotations about an arbitrary axis

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