A new method for solving the one-dimensional Schrödinger equation

As is well known, the solution of the one-dimensional Schrödinger equation enables one to formulate simple models for the description of phenomena in condensed matter physics. This equation can be solved analytically only for particular potentials. In this paper we describe a new method to solve the one-dimensional Schrödinger equation for a special class of potentials. The method presented here is almost analytic and gives a prescription for computer calculations of the eigenfunctions and eigenvalues.