A point mass attached to a spring with spring constant k = mω2. In classical mechanics the energy is continuous and the lowest state is one of being “at rest.” Solved quantum mechanically, the energy becomes discrete, E = (n + 1/2)ħω, and what is more, it cannot come to rest even in the lowest state.
In every figure the horizontal axis is the same position x (the equilibrium position is 0). The weight on the spring at the top and the wave function below it correspond directly: one sits exactly above the other.