1. Physics 452 Quantum mechanics II Winter 2012 Karine Chesnel

2. Homework Phys 452 Tuesday Jan 24: Homework # 5 Pb 6.12, 6.13, 6.14, 6.33 Thursday Jan 26: Homework # 6 Pb 6.16, 6.17, 6.18, 6.21

3. Phys 452 The fine structure of hydrogen Relativistic correction Pb 6.12 Pb 6.33 Pb 6.13 For example (1s) Introducing the azimuthal quantum number

4. Phys 452 Quiz 6d What is the relativistic correction for the band (3d)? A. B. C. D. E.

5. Phys 452 The fine structure of hydrogen Relativistic correction + Bohr’s energy E = Spin-orbit coupling + Fine structure

6. Phys 452 Quiz 7a What is the physical nature of the spin-orbit coupling effect ? A.An interaction between the spin of the electron and its orbital angular momentum B. An interaction between the spin of the electron and the orbital angular momentum of the nucleus C. An interaction between the spin of the electron and the spin of the nucleus D. An interaction between the spin of the nucleus and its orbital angular momentum E. An interaction between the spin of the nucleus and orbital angular momentum of the electron

7. Phys 452 The spin-orbit coupling Interaction between the spin S and the orbital angular momentum L of the electron in the hydrogen atom Magnetic interaction S SL Hamiltonian ? “Classical view” B e+e+ e-e-

8. Phys 452 The spin-orbit coupling Expressing the magnetic field in terms of L “Classical view” B e + or e - I r L

9. Phys 452 The spin-orbit coupling Connecting the magnetic moment M to the spin S “Classical view” e-e- M,S Gyromagnetic factor Quantum result: (relativistic quantum theory)

10. Phys 452 The spin-orbit coupling Taking the non-inertia of the electron frame into account: (Thomas precession) Final magnetic interaction

11. Phys 452 The spin-orbit coupling Using the total angular momentum J… Pb 6.16

12. Phys 452 The spin-orbit coupling First-order correction to the energies: (Pb 6.35)

13. Phys 452 The fine structure of hydrogen Combining S-O coupling with relativistic correction Pb 6.17

14. Phys 452 The fine structure of hydrogen New relevant quantum numbers: n, l, s, j and m j Pb 6.18 E Total energy value:

15. Phys 452 Quiz 8a Does the fine structure correction lift the degeneracy of the atomic levels ? A. Not at all B.Yes, partially C.Yes, completely D. It depends on the speed of the electron E. It depends on external fields

16. Phys 452 Quiz 8b For a given (n, l, j), what is the degeneracy of the level E nj ? A. B. C. D. E.

17. Phys 452 The spin-orbit coupling: physical evidences