We have a better model, but it's an ecuation so horrible that nobody want to solve it. Luckly, sometimes the exact solution can be very accuately aproximated w

We have a better model, but it's an ecuation so horrible that nobody want to solve it. Luckly, sometimes the exact solution can be very accuately aproximated with a wave ecuation. Luckly, sometimes the exact solution can be very accuately aproximated with a particle ecuation. (Sometimes, the exact solution can be aproximated saying that the lowest energy state is an eigenvector of the Schoedinger equation. Is that a wave? It's not localized, but not very wavy.) But neither are the exact solution, just aproximations that solve tpgether 99% of the experiment. It's difficult to explain, because to explaing the detials you need like two years of algebra and calculus and then like another 2 years of physics, and now you get a degree in physics. It's possible to solve the difficult ecuation only in very simple cases like electron-electron colissions, if you allow some cheating and a tiny error. For more complicated systems like electron-muon there are some problems. And for more complicated systems, you get more technical problems and more aproximations.