TRANSFER-MATRIX FOR THE ONE-DIMENSIONAL SCHRODINGER-EQUATION

A method based on the transfer matrix is used to relate the solutions of the Schrodinger equation in regions with zero values of the potential. It is shown that the transfer matrix is governed by six parameters: the de Broglie wavelength corresponding to a free particle, the coordinates of the left- and right-hand boundaries of a potential barrier (across which the solution is ''transferred''), the transmission coefficient, and the phase characteristics of the transmitted and reflected waves. The last three nontrivial parameters are calculated using recurrence relations. The expressions necessary for the investigation of potential barriers with a step on the right are also obtained. The proposed method making it possible to study resonant tunneling in one-dimensional quantum systems, for which the potential and the effective mass of a particle can be represented by piecewise-continuous functions of the spatial variable.