A novel numerical technique for solving the one-dimensional Schroedinger equation using matrix approach-application to quantum well structures

A numerical technique that allows straightforward determination of bound-state and quasi-bound-state energy eigenvalues (and lifetimes of the latter) for arbitrary one-dimensional potentials is presented. The method involves straightforward multiplication of 2×2 matrices and does not involve any iterations. The applicability of the technique to analysis of the quantum-well structures is also shown. Since the Schroedinger equation for a spherically symmetric potential can be transformed to a one-dimensional equation, all such problems can also be solved using this method