Application of the Rayleigh-Schrödinger Perturbation Theory to the Hydrogen Atom

Abstract

The motion of a single electron in the electrostatic field of a nucleus is treated by the Rayleigh-Schrödinger perturbation method, the whole electrostatic potential being considered as the “perturbation.” The contribution of the first approximation to the energy vanishes. The second approximation gives a finite ionization energy which is, however, incorrect numerically. The first approximation also vanishes for potentials ~r ⁻ⁿ with 0 < n < 3 but the second approximation is finite only for n = 1 : it vanishes for n > 1, and is infinite for n < 1.