© Daniel Kleppner.
These wave modes, which correspond to the three lowest energy de Broglie waves of a particle moving in a one-dimensional box (defined by the purple bars), are identical to the patterns for the modes on a string in Figure 9. The waves on a string result from the physical displacement of the string from equilibrium. The physical meaning of de Broglie waves is yet to be discussed. Nevertheless, their existence immediately leads to the concept of energy quantization. In this case, the energy levels increase as n2. (Unit: 5)