Variational R -matrix method for quantum tunneling problems

Abstract

A variational R-matrix method for solving the one-dimensional time-independent Schrödinger equation is presented. The theory is simple and general and applies to an arbitrary potential. As an example, the method is applied to the pedagogically important problem of quantum tunneling through a barrier. Accurate transmission and reflection coefficients are obtained by the variational R-matrix method which compare favorably with the known analytical solutions.