Angular momentum structure of the scattering phase shift

The partial-wave analysis of the quantum-mechanical scattering of a particle by a spherically symmetric potential is considered for continuous angular momentum, in contrast to the usual treatment where the angular momentum is discrete. Numerical illustrations of the scattering phase shift as a function of real, continuous angular momentum are presented. The scattering phase shift is calculated for Yukawa and exponential potentials of various strengths and ranges, and the properties of the phase shift (considered as a function of real, continuous angular momentum) are linked to the bound states and resonances of the quantum-mechanical system. Considering the phase shift as a function of continuous angular momentum eliminates the need to consider an infinite number of individual phase shifts and thus significantly simplifies the partial- wave description of the particle motion