  Energy resonance in scattering is usually investigated either directly in the
complex energy plane (E-plane) or indirectly in the complex angular momentum
plane (L-plane). Another formulation complementing these two approaches was
introduced recently. It is an indirect algebraic method that studies resonances
in a complex charge plane (Z-plane). This latter approach will be generalized
to provide a unified algebraic treatment of resonances in the complex E-, L-,
and Z-planes. The complex scaling (rotation) method will be used in the
development of this approach. The resolvent operators (Green's functions) are
formally defined in these three spaces. Bound states spectrum and resonance
energies in the E-plane are mapped onto a discrete set of poles of the
respective resolvent operator on the real line of the L- and Z-planes. These
poles move along trajectories as the energy is varied. A finite square
integrable basis is used in the numerical implementation of this approach.
Stability of poles and trajectories against variation in all computational
parameters is demonstrated. Resonance energies for a given potential are
calculated and compared with those obtained by other studies.
