An approach to solving the problems on transmission of material particles (e.g., molecules) through composite complex-shape potential barriers is proposed. To this end, a novel computational technique for integrating the Schrödinger equation is developed, which is based on the use of a non-standard matrix-analysis procedure and shows a good promise of being generalized to include two- and three-dimensional wave-dynamics problems. A good agreement is demonstrated between the results obtained using this approach and exact solutions for the transmission coefficient of a rectangular barrier. In the cases of particles or energy waves penetrating composite potential barriers, a quantum character of the membrane penetrability increasing as a function of the particle or wave energy is revealed. It is found that for the particles or photons of certain energies their transmission ratio could be increased by a factor of 2 or 3 via the use of new energy barriers added to the membrane.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 119–126, January, 2017.
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Bubenchikov, A.M., Bubenchikov, M.A., Potekaev, A.I. et al. Penetration of Microparticles Through Composite Potential Barriers. Russ Phys J 60, 140–148 (2017). https://doi.org/10.1007/s11182-017-1052-4
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DOI: https://doi.org/10.1007/s11182-017-1052-4