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A detailed analysis has been made by R.Zavin and N.Moiseyev(2004 J. Phys. A:Math, Gen, \textbf{37} 4619) for the change of bound states into resonancestates via coalescence of virtual states in a one-dimensional symmetricrectangular attractive potential as it becomes shallow, with convergent wavefunctions of virtual and resonance states by the complex scaling method. As acomplement to such an analysis, we discuss some global features of the polespectrum of the S-matrix by using a complex extension of the real potential$V^{(\mathrm{real})}$ to $e^{i\alpha}V^{(\mathrm{real})}$ with a real phase$\alpha$. We show the structures of trajectories of poles developed for thechange of $\alpha$ in the complex momentum plane, which is useful to understandthe mutual transformation among the bound, virtual and resonance states.

Mutual transformation among bound, virtual and resonance states in one-dimensional rectangular potentials