The Equation of Atom Motion in an External Gravitational Field

TL;DR

This paper demonstrates that the motion of a multielectron atom in an external gravitational field can be accurately described by the Mathisson-Papapetrou equations when using the expectation value of the total angular momentum, including spins and orbital momenta.

Contribution

It establishes a link between quantum angular momentum and classical equations of motion for atoms in gravitational fields, extending the applicability of the Mathisson-Papapetrou equations.

Findings

Motion of multielectron atoms follows Mathisson-Papapetrou equations in gravitational fields

Classical angular momentum includes spins and orbital momenta

Approximation holds under good conditions

Abstract

It is shown that the motion of a multielectron atom in an external gravitational field in a good approximation is described by system of the Mathisson-Papapetrou equations, if we put as a classical angular momentum of the atom the expectation value of the operator of the full angular momentum of the system, which includes spins of the nucleus and electrons, and orbital momentums of the electrons in the atom.