For a plane wave propagating in space: Ψ Ψ ( r , t ) = A e i ( k ⋅ ⋅ r − − ω ω t ) the probability density is constant everywhere; ρ ρ ( r , t ) = | A | 2 → → ∂ ∂ | Ψ Ψ | 2 ∂ ∂ t = 0 (that is, plane waves are stationary states) but the probability current is nonzero – the square of the absolute amplitude of the wave times the particle's speed; j ( r , t ) = | A | 2 ℏ ℏ k m = ρ ρ p m = ρ ρ v