Regge trajectory

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.

The simplest example of Regge poles is provided by the quantum mechanical treatment of the Coulomb potential ${\displaystyle V(r)=-e^{2}/(4\pi \epsilon _{0}r)}$ or, phrased differently, by the quantum mechanical treatment of the binding or scattering of an electron of mass ${\displaystyle m}$ and electric charge ${\displaystyle -e}$ off a proton of mass ${\displaystyle M}$ and charge ${\displaystyle +e}$. The energy ${\displaystyle E}$ of the binding of the electron to the proton is negative whereas for scattering the energy is positive. The formula for the binding energy is the well-known expression

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