The Schrödinger equation ensures that wave functions always change smoothly—the number that a wave function assigns to a particular location never hops instantly from 5 to 500. Instead, the numbers flow perfectly predictably: 5.1, 5.2, 5.3, and so on. A wave function’s numbers can go up and down again, like a wave—hence the name—but they’ll always undulate smoothly like waves too, never jerking around too crazily.
Wave
