In [J. A. Rebou\c{ c}as and P. A. Brand\~{ a}o, Phys. Rev. A 104, 063514 (2021)] the authors compute the scattering amplitude for a $\mathcal{ P}\mathcal{ T}$-symmetric double-delta-function potential in three dimensions by invoking the far-zone approximation and summing the resulting Born series. We show that the analysis of this paper suffers from a basic error. Therefore its results are inconclusive. We give an exact closed-form expression for the scattering amplitude of this potential.
Categories: quant-ph physics.optics