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We present a new approach to the quantum-classical problem, which treats itas the problem of modelling the quantum phenomenon described by a coherentsuperposition of microscopically distinct substates (CSMDS) as a compound oneconsisting of alternative subprocesses creating unremovable contexts for eachother, or as that of reducing a non-Kolmogorovian quantum probability space tounderlie a CSMDS to the sum of Kolmogorovian ones. We develop such models for a1D completed scattering and double slit diffraction. The quantum-classicalproblem disappears when, in quantum theory with its integral superpositionprinciple, CSMDSs obey the "either-or" rule to guide alternative random events.There is no observable which could be associated with the whole ensemble ofstatistical data described by a CSMDS, because such data are incompatible -- inthe case of a CSMDS, any observable splits into noncommuting observablesassociated with the substates. To calculate the average value of any observableas well as to introduce characteristic times is meaningful only for thesubstates of a CSMDS. Ignoring this feature in the conventional description ofCSMDSs just leads to paradoxical results (e.g., to the Hartman effect andpassing a particle through two slits in the screen simultaneously).

From a 1D completed scattering and double slit diffraction to the quantum-classical problem: A new approach