In my first Physics class (in high school by the way, a huge shame that i had so little before college), the first thing we talked about was the physics of elastically colliding bodies that have no interaction between them at all. However, I've only ever analyzed such systems with force diagrams, never with Hamiltonians and Lagrangians. And I've certainly never talked about the quantum mechanical systems. I imagine that I could try taking the limit of a coulomb repulsion potential (of a system of like charged particles as the charge goes to 0 maybe?) So how about it? How do I handle this system Quantum Mechanically? I suspect that fermions do this automatically (do they?), and bosons of course do not (which is a nice thing about them). But how do I do this in the case of distinguishable particles?