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It is shown that in the state space of a quantum particle involved in aone-dimensional completed scattering (OCS) there is a superselection rule (SSR)induced by the dichotomous physical context that determines the properties of aquantum ensemble of scattering particles in the disjoint spatial regionslocated on the different sides of the potential barrier at asymptotically largedistances from it. At the initial stage of the OCS this context is associated,in the general case, with two sources of particles located on the differentsides of the barrier; and at the final stage it is associated, in the generalcase, with two particle detectors located on different sides of the barrier.The role of a superselection operator is played by the Pauli matrix $\sigma_3$that divides the space of in- and out-asymptotes into two coherent sectors. Inthe course of the OCS, its unitary quantum dynamics crosses these sectors. Inparticular, in the scattering problem with one source and two detectors, a pureinitial state of a particle is converted into a mixed final state. According tothis rule, the OCS is a complex quantum process consisting of two coherentsubprocesses -- transmission and reflection; the average value of anyobservable as well as characteristic times can be defined for the subprocessesonly. It is shown that the quantum dynamics of both subprocesses at all stagesof scattering is uniquely determined by the initial state of the whole ensembleof particles and by the final states of transmitted and reflected particles.

Dichotomous-context-induced superselection rule for a one-dimensional completed scattering