16 - The Electronic States of Atoms. I. The Hydrogen Atom and the Simple Orbital Approximation for Multielectron Atoms

Abstract

The Schrödinger equation for the hydrogen atom is an example of the “central-force problem,” in which the potential energy depends only on the distance between the two particles that make up the system. In the central-force problem, the angular momentum of the system can have definite values if the system is in a state corresponding to an energy eigen function. The Schrödinger equation for the hydrogen atom can be solved exactly, giving electronic wave functions called orbitals. Electrons have intrinsic (spin) angular momentum in addition to the angular momentum of orbital motion. Spin orbitals describe both space and spin behavior. Each electron in a multielectron atom occupies a hydrogen-like spin orbital if the simple orbital approximation is applied. The wave function for a multielectron atom must be antisymmetric. According to the Pauli exclusion principle, in an orbital wave function every electron must occupy a different spin. The total orbital angular momentum and the total spin angular momentum correspond to the same pattern as other angular momenta, and are used to characterize the energy levels of multielectron atoms.