Scattering theory is a branch of theoretical physics that deals with the study of how particles interact and scatter off of each other or off of potential energy barriers. It is often used to analyze the behavior of waves or particles when they encounter obstacles or potential energy barriers in various systems, such as quantum mechanics, acoustics, or electromagnetism. Scattering theory can provide insights into fundamental properties of particles, such as their energy levels, potential interactions, and the structure of the medium through which they are propagating. The mathematical techniques used in scattering theory can vary depending on the specific system being studied, but common approaches include solving partial differential equations, wave equations, or using techniques from functional analysis and quantum mechanics.