The de Broglie relationship tells us that particles behave like waves too.
-An electron has a wavefunction $\psi$ associated with it. The intensity of the wavefunction tells us where we have more chances of finding the electron.
When the electron is confined, its wavefunction shows standing wave patterns and the wavelength of the electron wavefunction is quantized. The rules for a particle in a box are the same as a standing wave.
This leads (via de Broglie's relationship) to a quantization of the momentum and the energy.
For an electron in a box, the energy levels go like the harmonic number squared.
You should be able to describe uncertainty and know what antimatter is.