A new approach in which tunneling of a quantum particle through a one-dimensional potential barrier is treated as a combined process involving two alternative elementary transmission and reflection processes is presented. It is demonstrated that the wave function describing the state of the entire quantum ensemble of particles can unambiguously be expressed as a sum of two other solutions of the one-dimensional Schrödinger equation (ODSE) that describe the states of sub-ensembles of transmitted and reflected particles in all stages of scattering.
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