Classical and quantum scattering
Most problems we have discussed so far, from harmonic oscillations to planet motion, are bound systems. There are unbound systems in our physical world, such as light scattering from water droplets making rainbows, as well as proton-proton collisions leading to the recent discovery of Higgs boson in the world's largest atom smasher. These are scattering problems. To study them, we need a fundamentally new approach to account for the fact that particles come in from infinity and go out to infinity.
Much of what we know about the fundamental forces (e.g., Coulomb, strong, and weak) comes from particle scattering studies. In a typical scattering setup, a beam of particles (projectiles), prepared in well-defined initial states, is sent to a target region for collisions with the constituents. After the beam passes through, the outgoing particles will be scattered relative to their incoming direction, possibly accompanied by other fragments or secondary emissions. By detecting the scattered particles, on the one hand, we can infer the underlying forces that caused the deflection or scattering. This was how the atomic nucleus was discovered in Rutherford's alpha-particle and gold-foil experiment. On the other hand, if the interaction forces are presumed to be well known, scattering studies can test and improve our understanding of collision dynamics by comparing experimental observations with theoretical models and predictions. The study of ...