The hydrogen atom according to wave mechanics - II. paraboloidal coordinates

Abstract

In the second of five parts in a series, the Schroedinger equation is solved in paraboloidal coordinates to yield amplitude functions that enable accurate plots of their surfaces to illustrate the variation of shapes and sizes with quantum numbers n1, n2, m, for comparison with the corresponding plots of amplitude functions in coordinates of other systems. A useful property of these functions in paraboloidal coordinates is their application to treat the Stark effect, when a hydrogen atom is placed in an isotropic electric field.