SOLVING THE SCHRODINGER-EQUATION IN ARBITRARY QUANTUM-WELL POTENTIAL PROFILES USING THE TRANSFER-MATRIX METHOD

We present a simple, accurate, and fast algorithm for solving the one-dimensional time-independent Schrodinger equation. The algorithm is based on the transfer matrix method. We can thus calculate all bound and quasi-bound energy levels and the corresponding wave functions for an arbitrarily shaped potential profile. The results of our calculations are compared with those obtained by other authors for various types of problems. A central part of this paper deals with the solving of the Schrodinger equation in quantum-well structures. Our 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 computers, such as a PC.