Light has both particle and wave properties at the same time. Likewise, de Broglie (France, 1892 - 1987) thought that such things as electrons which had so far been considered to be particles might possess wave nature as well (1932). This is the idea of the de Broglie waves or de Broglie's matter waves.

Let us consider a hydrogen atom with Bohr's quantum theory. In that theory, the quantum condition to determine the stationary states of the atom seems to claim that the circumference of the orbit of the electron revolving about the nucleus should be an integral multiple of the wavelength of the de Broglie wave of the electron.

This quantum condition says that the de Broglie wave of the electron must be a continuous standing wave around the nucleus.

In right figure, the de Broglie wave does not connect smoothly, because the circumference is not an integral multiple of the wave length. Namely, the right figure does not show a correct de Broglie wave in a hydrogen atom.