To be used in future

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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.