Levinson's theorem

Levinson's theorem relates the number of bound states (stable energy levels) in a quantum system to the behavior of its scattering process at zero energy. Essentially, it states that by examining how particles scatter off a potential at very low energies, you can determine how many bound states the system has. If the scattering phase shift (a measure of how the wave is altered) changes by a certain amount as energy approaches zero, it indicates the presence of a specific number of bound states. This connection helps physicists understand the relationship between observable scattering phenomena and the internal energy structure of the system.