Regge theory
In quantum physics, Regge theory is the study of the analytic properties of scattering as a function of angular momentum, where the angular momentum is not restricted to be an integer but is allowed to take any complex value. The nonrelativistic theory was developed by Tullio Regge in 1959.
History and implications
The main result of the theory is that the scattering amplitude for potential scattering grows as a function of the cosine 
of the scattering angle as a power that changes as the scattering energy changes:
where 
is the noninteger value of the angular momentum of a would-be bound state with energy 
. It is determined by solving the radial Schrödinger equation and it smoothly interpolates the energy of wavefunctions with different angular momentum but with the same radial excitation number. The trajectory function is a function of 
for relativistic generalization. The expression 
is known as the Regge trajectory function, and when it is an integer, the particles form an actual bound state with this angular momentum. The asymptotic form applies when is much greater than one, which is not a physical limit in nonrelativistic scattering.
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