Poles, bound states, and resonances illustrated by the square well potential

Poles of the S matrix in the complex momentum plane are known to be related to the bound states, virtual states, and transmission resonances of the potential. We illustrate this by tracing the motion of the poles in the case of a square well in one dimension. The conditions for appearance of prominent resonances are clarified. It is shown that the graphical solution due to Pitkanen provides the virtual or antibound states as well as the bound states. A near‐threshold formula for the binding energies is presented that also works for the antibound states.