Assuming the field is weak and the motion of the electron non-relativistic, we have the total energy of the electron approximately equal to its rest energy, and the momentum reducing to the classical value, E − − e ϕ ϕ ≈ ≈ m c 2 p ≈ ≈ m v and so the second equation may be written ψ ψ − − ≈ ≈ 1 2 m c σ σ ⋅ ⋅ ( p − − e c A ) ψ ψ +