Non‐Hermitian Hamiltonians are used in many research areas as approximate models of physical systems, for example, the optical‐model potential in nuclear physics. Such Hamiltonians are rarely treated in introductory quantum mechanics. Here the quantum scattering problem of a two‐state system is treated exactly for the case of one‐dimensional square‐well potentials. By introducing an appropriate optical‐model potential, an approximate solution for one of the two states is obtained. The exact and approximate solutions are compared for a realistic example.

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