As for all quantum particles free or bound, the Heisenberg uncertainty principles Δ Δ p x Δ Δ x ≥ ≥ ℏ ℏ 2 apply. It is clear that since the plane wave has definite momentum (definite energy), the probability of finding the particle's location is uniform and negligible all over the space. In other words, the wave function is not normalizable in a Euclidean space, these stationary states can not correspond to physical realizable states.