Physics 452 Quantum mechanics II Winter 2011 Karine Chesnel

Homework Phys 452 Thursday Jan 27: Homework # 6 Pb 6.16, 6.17, 6.18, 6.21

Phys 452 Quiz 8a Which statement is true regarding the spin-orbit coupling? A.The SO coupling is the effect of an external magnetic field on the spin of the electron B. The SO coupling does not occur in the presence of an external magnetic field C. The SO coupling includes the relativistic correction D. The SO coupling describes the interaction between different angular momenta E. The SO coupling is magnetic interaction that lift completely the degeneracy of atomic levels

Phys 452 The spin-orbit coupling Magnetic interaction SL Interaction between the spin S and the orbital angular momentum L of the electron in the hydrogen atom S “Classical view” B e+e+ e-e- Pb 6.16

Phys 452 The spin-orbit coupling First-order correction to the energies: Perturbation:

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

Phys 452 The fine structure of hydrogen New relevant quantum numbers: n, l, s, j and m j Pb 6.18 E Total energy: Pb 6.17

Phys 452 Quiz 8b 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

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

Phys 452 Zeeman effect Effect of an external field “Classical view” e-e- S L B ext

Phys 452 Zeeman effect “Classical view” e-e- S L B ext Weak-field Strong field Intermediate field Fine structure dominates Zeeman effect dominates Comparing:and Pb 6.20

Phys 452 Zeeman effect Weak -field e-e- S L B ext Good eigenstates: with Lande factor: Pb 6.21

Phys 452 Zeeman effect e-e- S L B ext Strong -field Good eigenstates: Pb 6.23,6.24

Phys 452 Zeeman effect e-e- S L B ext intermediate -field Clebsch-Gordan Pb 6.25