We discuss the properties of the partial wave S-matrix in the complex momentum and complex energy plane. We establish that bound states appear as poles in these planes. The relation between resonances and bound states are also discussed.

In this section we discuss how the bound state energies in a given angular momentum state are related to the poles in the complex energy plane of the scattering amplitude in that state. As an illustration we consider a square well potential given by

and consider specifically an *S*-wave (*l* = 0) bound state. Here we have *E* < 0, so ...

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