A New Approach to Tunneling

Abstract
A new numerical algorithm for tunneling is presented. This algorithm can be used to analyse an onedimensional potential barrier with an arbitrary profile. It is able to calculate not only the transmission coefficient accurately, but also the phases of the transmitted and reflected waves. Using the Schrodinger equation and plane waves, we introduce a tunneling matrix to relate the transmitted and incident wave functions. Thus the transmission coefficient and phase can be calculated from the tunneling matrix.To test the accuracy of this algorithm,we calculate the transmission coefficients and phases for a double -barrier (resonant tunneling) and a triangular barrier (field emission), and make comparisous with corresponding analytical values. It shows that this algorithm is fast, accurate and efficient.