ABSTRACT
This chapter looks at a class of problem for which the series concerned are convergent, in the sense of formal mathematics, but give slow convergence when they are simply 'added up' directly. As a necessary preliminary to explaining the method the author sets out some useful forms of the one-particle Schrodinger equation, including a slightly unusual form of the radial equation which turns out to be particularly appropriate for use with the finite-difference methods. For both the harmonic oscillator and the hydrogen atom the eigenfunctions take the form of an exponential factor multiplied by a polynomial. However, it is not the finite number of terms which matters. Readers with sufficient experience to have developed their own programming style may not agree with every detail in the author's program, but he/she think that any effective program for the power series method must conform fairly closely to the following flowchart.
