1.3.1 Pauli Equation

Let us denote the electron energy after subtracting its rest energy by E′, i.e., E′=E-mc2. For the non-relativistic motion of electron in a station-ary magnetic field A(r)=0, V=0, you can assume |E′| ≪ mc2. Then Eq. (1.46)reduce to

Substituting the value of χ from (1.48) into (1.47), you get an equation containing the two-component wavefunction φ only

With the help of the formula(1.27)you have

Since ∇× A=B is the magnetic field, you obtain the non-relativistic equation for an electron moving in a magnetic field

This is called Pauli equation for it was first proposed by Pauli in 1927. You can interpret that the Zeeman term in(1.50)is due to the interaction energy between the applied magnetic field and the magnetic moment taken by the electron. Thus you perceive that the magnetic moment of electron spin, µ=µ0σ (where µ0= is the Bohr magneton), is a natural consequence of relativity and quantum mechanics, and not simply an add-on to explain atomic spectra.