In Book 1 Millie wonders about the location of the electron that transformed into a wave. The answer she receives is: "Probably not far, but it could be anywhere."
The word probably was not chosen by chance. In fact, it is impossible to know exactly where the electron is. But we can ask: "what is the probability of finding the electron in a specific place?". Millie learns that the electron could be anywhere within the wave, but not all points are equal. The probability of finding the electron is not the same everywhere. In 1926, the Austrian physicist and Nobel Prize winner Erwin Schrödinger managed to associate a probability wave with each particle. The intensity of the probability wave at a given point in space provides the probability of finding the particle at that point.
Imagine you’re looking for your cat, but instead of knowing exactly where it is, you have a map that shows you all the places the cat might be: maybe it's on the couch, under the table, or near the window. Some spots on the map are darker, meaning it's more likely to be there, but you won't know for sure until you actually find it.
The probability wave is like that map, but for a particle. It tells us all the places the particle might be, with some places being more likely than others. And until we look, the particle isn’t in one place: it’s kind of spread out in a blurry cloud, like it’s playing hide and seek!
Schrödinger called this probability wave the wave function and described its behavior with the famous Schrödinger equation, which is fundamental in quantum physics. The wave function is represented by the Greek letter Ψ, pronounced "psi," which is why the electron shouts Psi to become a wave.
Since particles do not always behave like waves, at some point, the waves turn into particles. This transformation is called the collapse of the wave function because the wave, which undergoes a collapse, disappears, and the particle appears. This is why, in Book 2, the electron shouts collapse to become a particle.