2.3 Fine structure

1. 2.3 Fine structure Relativistic effects lead to small splittings of the atomic energy levels called fine structure. We estimated the size of this structure in Section 1.4 by comparing the speed of electrons in classical orbits with the speed of light. In this section we look at how to calculate fine structure by treating relativistic effects as a perturbation to the solutions of the Schrodinger equation. This approach requires the concept that electrons have spin.

2. 2.3.1 Spin of the electron_1 In addition to the evidence provided by observations of the fine structure itself, that is described in this section, two other experiments showed that the electron has spin angular momentum, not just orbital angular momentum. One of these pieces of experimental evidence for spin was the observation of the so-called anomalous Zeeman effect. For many atoms, e.g. hydrogen and sodium, the splitting of their spectral lines in a magnetic field does not have the pattern predicted by the normal Zeeman effect (that we found classically in Section 1.8). This anomalous Zeeman effect has a straightforward explanation in terms of electron spin (as shown in Section 5.5). The second experiment was the famous Stern-Gerlach experiment that will be described in Section 6.4.1.

3. 2.3.1 Spin of the electron_2

4. 2.3.1 Spin of the electron_3

5. 2.3.1 Spin of the electron_3

6. 2.3.1 Spin of the electron_4

7. 2.3.2 The spin-orbit interaction_1

8. 2.3.2 The spin-orbit interaction_2

9. 2.3.2 The spin-orbit interaction_3

10. 2.3.2 The spin-orbit interaction_4

11. 2.3.2 The spin-orbit interaction_5

12. 2.3.2 The spin-orbit interaction_6

13. 2.3.2 The spin-orbit interaction_7

14. 2.3.2 The spin-orbit interaction_8

15. 2.3.3 The fine structure of hydrogen_1

16. 2.3.3 The fine structure of hydrogen_2

17. 2.3.3 The fine structure of hydrogen_3

18. 2.3.3 The fine structure of hydrogen_4

19. 2.3.3 The fine structure of hydrogen_5 0 E(v)=mc2 (1.16)

20. 2.3.3 The fine structure of hydrogen_6

21. 2.3.4 The Lamb shift_1

22. 2.3.4 The Lamb shift_2

23. 2.3.4 The Lamb shift_3

24. 2.3.4 The Lamb shift_4

25. 2.3.4 The Lamb shift_5

26. 2.3.5 The Transitions between fine-structure levels_1 Transitions in hydrogen between the fine-structure levels with principal quantum numbers n=2 and 3 give the components of the Balmer-aline shown in Fig. 2.7; in order of increasing energy, the seven allowed transitions between the levels with different j are as follows:

27. 2.3.5 The Transitions between fine-structure levels_2