We can simplify over q to obtain ∂ ∂ ε ε n ∂ ∂ k = ℏ ℏ 2 m ∫ ∫ d r u n k ∗ ∗ ( − − i ∇ ∇ + k ) u n k and we can reinsert the complete wave functions ∂ ∂ ε ε n ∂ ∂ k = ℏ ℏ 2 m ∫ ∫ d r ψ ψ n k ∗ ∗ ( − − i ∇ ∇ ) ψ ψ n k