Abstract
A generalized Schrödinger approximation, due to Ikhdair & Sever, of the semi-relativistic two-body problem with a rectangular barrier in (1+1) dimensions is compared with exact computations. Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers. The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |ϵ − V0| < 2μc2, where μ is the reduced mass, ϵ the scattering energy, and V0 the barrier top energy. The approximate wave numbers are less accurate.
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