ABSTRACT
This chapter gives a brief sketch of some parts of Rayleigh-Schrödinger perturbation theory, the author have written in detail about perturbation theory elsewhere and concentrate here on a few ideas which are directly useful in numerical work on a microcomputer. The intellectual puzzle of how to reduce everything to an energy calculation gets really interesting if we want to calculate a local quantity, e.g. the value of the (normalised) wavefunction at the origin. The renormalised series trick seems to give the results to greater accuracy and more easily. The program makes an essential use of arrays, but since the array subscripts on the Pet cannot be negative the subscripts have to be changed from their values in the theoretical equations. In many-body theory, then, the sum-overstates formalism can be useful for giving a semi-quantitative account of various important effects, and the so-called diagrammatic perturbation theory used in atomic theory leans heavily on that formalism.
