The stability of a wavefunction under a perturbation

Abstract

Abstract The concept of the stability of a wavefunction under a perturbation is defined and the properties which distinguish stable wavefunctions are deduced. The stability of approximate wavefunctions 18 particularly examined and a number of general results stated. Self-consistent wavefunctions are shown to be stable under one electron perturbations. The concept enables many hitherto isolated results to be unified and extended. In particular a new method of calculating nuclear magnetic shielding Constants for atoms is given. The concept also suggests means of improving an approximate wavefunction so that the derived estimate of some property is made more accurate.