The Solution of the Schrödinger Equation for an Approximate Atomic Field

Abstract

An approximate atomic potential having an "effective nuclear charge for potential," that is, bilinear in the radial distance from the nucleus, is discussed and shown to approximate reasonably well to Hartree or Fermi-Thomas potentials. The Schrödinger equation with the approximate potential is solved as a series of hydrogenic wave functions and as a power series in $\frac{\mathrm{Ar}}{\mathrm{}(1+Ar)\mathrm{}}$ ($A$ being a parameter of the potential). Some illustrative numerical results pertaining to the mercury atom are presented.