= Redundant pole of a scattering matrix
A pole of a <scattering matrix> arising from the numerator $F(-k)$ rather than a zero of the incoming <Jost function> $F(k)$ can fail to correspond to a <bound state>. For $F(k)=(k-i\kappa)/(k+i\alpha)$, the pole at $i\kappa$ is associated with the incoming zero; the pole at $i\alpha$ comes from the numerator. The regular Eckart realization has $\alpha>\kappa$. The distinction and this explicit example are discussed in https://dipot.ulb.ac.be/dspace/bitstream/2013/373712/4/2306.12216.pdf.
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