Solving the Schrodinger equation in arbitrary quantum-well potential profiles using the transfer matrix method

A simple, accurate, and fast algorithm for solving the one-dimensional time-independent Schrodinger equation is presented. The algorithm is based on the transfer matrix method. This makes it possible to calculate all bound and quasi-bound energy levels and the corresponding wave functions for an arbitrarily shaped potential profile. The results of calculations are compared with those obtained by other authors for various types of problems. A central part of this study deals with solving the Schrodinger equation in quantum-well structures. The results show that the transfer matrix method is as accurate as other methods, but it is easier to implement and, hence, is superior for calculations on small computer, such as a PC