Popular science books often explain the essence of quantum mechanics by the statement: "The electron is both a particle and a wave". But what does this statement mean?
We have already seen that the electron is described by a wave. The word 'particle' suggests something that is a pointlike object, moving according to Newton's laws of motion. But we will see that this is not the sense in which the electron is a particle in quantum mechanics.
By the time quantum mechanics came around, scientists had become used to the idea that particles were discrete: you can have no electron or one electron, but you cannot have half an electron. We will see that all waves in quantum theory exhibit a similar discreteness. This is the meaning of saying that the electron has a particle-like behavior.
Once we understand both the wave nature of the electron and the discreteness of this wave, we will be able to turn to the puzzles that emerge from these two aspects of the electron.