A simple iterative solution of the Schroedinger equation in matrix representation form

A simple procedure for solving the Schroedinger equation is presented. It is based upon an iterative solution of the secular equation. A large enough convergence rate is obtained by using a basis set of properly scaled functions. The effect of the scaling parameter on the convergence rate is studied in order to improve the calculation. The method is applied to simple, though non-trivial, quantum mechanical models such as the quartic, sextic and octic anharmonic oscillators, a double well potential, and the linear confining potential. Highly accurate eigenvalues for all values of the coupling parameter are obtained. (author)