Abstract
In this paper, we investigate phase rigidity of one-dimensional point interactions. With the aid of supersymmetric quantum mechanics (SUSYQM) we generate family of isospectral potentials describing point interactions. We than demonstrate that for SUSYQM generated bound states in the continuum (BIC) phase rigidity is always zero, while for bound states from discrete part of spectrum phase rigidity may vary from zero to unity, depending on the strength of point interaction.
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