Using the following ansatz: ( ψ ψ 1 ψ ψ 2 ) = e − − i m c 2 t ℏ ℏ ( ψ ψ χ χ ) , with two new spinors ψ ψ , χ χ , the equation becomes i ℏ ℏ ∂ ∂ t ( ψ ψ χ χ ) = c ( σ σ ⋅ ⋅ Π Π χ χ σ σ ⋅ ⋅ Π Π ψ ψ ) + q ϕ ϕ ( ψ ψ χ χ ) + ( 0 − − 2 m c 2 χ χ ) .