© Daniel Kleppner.
The blue lines (a-d) show the n = 1, 3, 5, and 7 wavefunctions for a particle in a one-dimensional box. The black line (e) is the sum of these wavefunctions, which itself is a solution of Schrödinger's equation. It is remarkable that four wiggly curves add to give a smooth curve, but the computation is highly precise. As additional curves of shorter wavelengths are added, the resultant peak becomes narrower and narrower. Thus, in principle, the particle can be precisely localized. However, the spread in momentum would be enormous. (Unit: 5)