On the Ehrenfest theorem of quantum mechanics

TL;DR

This paper provides a rigorous mathematical derivation of Ehrenfest's equations for quantum systems, including complex atomic and molecular Hamiltonians with Coulomb interactions, clarifying foundational aspects of quantum mechanics.

Contribution

It offers the first rigorous derivation of Ehrenfest's equations applicable to general quantum Hamiltonians with Coulomb interactions.

Findings

Ehrenfest's equations are valid under broad conditions.

The derivation includes atomic and molecular Hamiltonians with Coulomb potentials.

Clarifies the mathematical foundations of quantum expectation value dynamics.

Abstract

We give a mathematically rigorous derivation of Ehrenfest's equations for the evolution of position and momentum expectation values, under general and natural assumptions which include atomic and molecular Hamiltonians with Coulomb interactions.