Compute ∇ ∇ ⋅ ⋅ A and apply the product rule for the ∇ operator, ∇ ∇ ⋅ ⋅ A = ∇ ∇ ⋅ ⋅ ( φ φ ∇ ∇ ψ ψ − − ψ ψ ∇ ∇ φ φ ) = ( ∇ ∇ φ φ ) ⋅ ⋅ ( ∇ ∇ ψ ψ ) + φ φ ∇ ∇ 2 ψ ψ − − ( ∇ ∇ φ φ ) ⋅ ⋅ ( ∇ ∇ ψ ψ ) − − ψ ψ ∇ ∇ 2 φ φ = φ φ ∇ ∇ 2 ψ ψ − − ψ ψ ∇ ∇ 2 φ φ .