Kantorovich and Galerkin-Type Methods for Modelling Quantum Tunneling of Composite Systems through Barriers

The description of quantum tunnelling of composite systems through repulsive barriers using the coupled-channel approximation of the adiabatic approach is presented. In this approach the multichannel scattering problem for the Schrödinger equation is reduced to a set of coupled second-order ordinary differential equations with the boundary conditions of the third type and solved using the R-matrix method. The efficiency of the proposed approach is demonstrated by the example of analyzing metastable states that appear in composite quantum systems tunnelling through repulsive barriers and give rise to the quantum transparency effect.