The wave function is a mathematical construct that doesn't actually have anything to say about the actually of a particle. It is, in essence, the probability of

The wave function is a mathematical construct that doesn't actually have anything to say about the actually of a particle. It is, in essence, the probability of where you might find the entity if you make measurements. As such to say that the electron is "smeared" around the atom is not saying anything meaningful about the electron. All we can say is that we don't know where it is. To attribute a dispersal property to the electron (or any other particle for that matter) is not doing anything helpful to discover or understand what an electron is.