Penetration of Microparticles Through Composite Potential Barriers

Abstract

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.