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*Shanxi University Atomic Physics 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. *Shanxi University Atomic Physics 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. *Shanxi University Atomic Physics 2.3.1 Spin of the electron_2 *Shanxi University Atomic Physics 2.3.1 Spin of the electron_3 *Shanxi University Atomic Physics 2.3.1 Spin of the electron_3 *Shanxi University Atomic Physics 2.3.1 Spin of the electron_4 *Shanxi University Atomic Physics 2.3.2 The spin-orbit interaction_1 *Shanxi University Atomic Physics 2.3.2 The spin-orbit interaction_2 *Shanxi University Atomic Physics 2.3.2 The spin-orbit interaction_3 *Shanxi University Atomic Physics 2.3.2 The spin-orbit interaction_4 *Shanxi University Atomic Physics 2.3.2 The spin-orbit interaction_5 *Shanxi University Atomic Physics 2.3.2 The spin-orbit interaction_6 *Shanxi University Atomic Physics 2.3.2 The spin-orbit interaction_7 *Shanxi University Atomic Physics 2.3.2 The spin-orbit interaction_8 *Shanxi University Atomic Physics 2.3.3 The fine structure of hydrogen_1 *Shanxi University Atomic Physics 2.3.3 The fine structure of hydrogen_2 *Shanxi University Atomic Physics 2.3.3 The fine structure of hydrogen_3 *Shanxi University Atomic Physics 2.3.3 The fine structure of hydrogen_4 *Shanxi University Atomic Physics 2.3.3 The fine structure of hydrogen_5 E(v)=mc2 (1.16) 0 *Shanxi University Atomic Physics 2.3.3 The fine structure of hydrogen_6 *Shanxi University Atomic Physics 2.3.4 The Lamb shift_1 *Shanxi University Atomic Physics 2.3.4 The Lamb shift_2 *Shanxi University Atomic Physics 2.3.4 The Lamb shift_3 *Shanxi University Atomic Physics 2.3.4 The Lamb shift_4 *Shanxi University Atomic Physics 2.3.4 The Lamb shift_5 *Shanxi University Atomic Physics 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
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