Levinson theorem

Levinson's theorem links the number of bound states in a quantum system to the phase shift experienced by scattering particles. When particles, like electrons, scatter off a potential, their wave functions change phase. Levinson's theorem states that the total change in this phase shift at zero energy corresponds directly to the number of bound states created by the potential. In essence, by measuring how much the wave function’s phase shifts, physicists can determine how many stable, bound particles exist within that potential, providing a powerful link between scattering data and bound state properties.