To be used in future
Section 4.5: Coupling of light to atoms and nuclei: multipole couplings Up Chapter 4: Charged Particles and Electromagnetic Fields Section 4.7: The Pauli-Schrödinger equation

4.6 Internal degrees of freedom: spin

Up to this stage we have not looked at internal degrees of freedom, but from the famous Stern-Gerlach experiment (particles with spin in a magnetic field), see Figs. 4.2↓,4.3↓, we know that the internal spin degree of freedom interacts in interesting ways with the magnetic field.
The effect can be described in an ad-hoc way by assuming that the spin degree of freedom (an angular momentum with magnitude ) is aligned by the magnetic field,. This is described by adding a term to the Hamiltonian. Here we have used the empirical value of the Bohr magneton, which we will derive now from first principles.
Section 4.5: Coupling of light to atoms and nuclei: multipole couplings Up Chapter 4: Charged Particles and Electromagnetic Fields Section 4.7: The Pauli-Schrödinger equation