The One-Electron Atom

Abstract

There is a fundamental difference between the theoretical approaches for atoms with at least two electrons, and systems with just a single electron. For any quantum mechanical problem, a preferred way to approach a problem is to formulate the Schrödinger equation and to solve it analytically. For hydrogen, this is feasible. For a system with a nucleus and two or more electrons, we have a multibody problem, and a direct assault on the Schrödinger equation is harder. For multielectron atoms, this book principally relies on perturbation theory. For this, we use the central-field approximation, where zeroth order states are products of individual electron wave functions. This makes the one-electron atom formalism relevant as a first stepping stone for the study of multielectron atoms, and we begin this book by a brief recapitulation of the hydrogen problem. This chapter also establishes important nomenclature, extensively used throughout the book.