The position operator is given by r ^ ^ = i ℏ ℏ ∂ ∂ ∂ ∂ p = i ∂ ∂ ∂ ∂ k with eigenfunctions ϕ ϕ r ( k ) = 1 ( 2 π π ) 3 e − − i k ⋅ ⋅ r and eigenvalues r. So a similar decomposition of ϕ ϕ ( k ) can be made in terms of the eigenfunctions of this operator, which turns out to be the inverse Fourier transform, ϕ ϕ ( k ) = 1 ( 2 π π ) 3 ∫ ∫ r -space ψ ψ ( r ) e − − i k ⋅ ⋅ r d 3 r .