Consider a particle in a one-dimensional box of length L . The eigenfunctions in position and momentum space are ψ ψ n ( x , t ) = { A sin ⁡ ⁡ ( k n x ) e − − i ω ω n t , 0 < x < L , 0 , otherwise, and φ φ n ( p , t ) = π π L ℏ ℏ n ( 1 − − ( − − 1 ) n e − − i k L ) e − − i ω ω n t π π 2 n 2 − − k 2 L 2 , where ω ω n = π π 2 ℏ ℏ n 2 8 L 2 m and we have used the de Broglie relation p = ℏ ℏ k . The variances of x and p can be calculated explicitly: σ σ x 2 = L 2 12 ( 1 − − 6 n 2 π π 2 ) σ σ p 2 = ( ℏ ℏ n π π L ) 2 .