On Langmuir's periodic orbit

TL;DR

This paper provides an analytic proof for the existence of Langmuir's periodic orbit in the classical three-body model of the helium atom, extending the understanding of classical orbits in atomic physics.

Contribution

It offers the first rigorous analytic proof of Langmuir's periodic orbit, previously established only numerically.

Findings

Analytic proof of Langmuir's periodic orbit

Supports classical models of atomic structure

Enhances understanding of three-body problem in physics

Abstract

Niels Bohr successfully predicted in 1913 the energy levels for the hydrogen atom by applying certain quantization rules to classically obtained periodic orbits. Many physicists tried to apply similar methods to other atoms. In his well-known 1921 paper, I.~Langmuir established numerically the existence of a periodic orbit in the helium atom considered as a classical three body problem. In this paper we give an analytic proof of the existence of Langmuir's periodic orbit.