Real understanding of general magnetism presumes a fundamental knowledge about atomic magnetism. We establish the electron spin and the spin–orbit interaction through the relativistic Dirac equation. With the help of the extremely useful Wigner–Eckart theorem, we can describe, quantitatively, the individual atomic electron, when it sees a spherically symmetric nuclear field and an external magnetic field. The usual assumption that the nucleus is a positive point charge imposes restrictions. Correction to this assumption leads to hyperfine interaction terms. While we can set up the Hamiltonian of a one-electron atom practically completely, the case of many-electron atom requires already first simplifications.
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