Suppose we have a three-dimensional wave function in position space ψ (r), then we can write this functions as a weighted sum of orthogonal basis functions ψ j (r) : ψ ψ ( r ) = ∑ ∑ j ϕ ϕ j ψ ψ j ( r ) or, in the continuous case, as an integral ψ ψ ( r ) = ∫ ∫ k -space ϕ ϕ ( k ) ψ ψ k ( r ) d 3 k It is clear that if we specify the set of functions ψ ψ k ( r ) , say as the set of eigenfunctions of the momentum operator, the function ϕ ϕ ( k ) holds all the information necessary to reconstruct ψ (r) and is therefore an alternative description for the state ψ ψ .