The semi-classical limit of the time dependent Hartree-Fock equation. II. The Wick symbol of the solution

TL;DR

This paper investigates the Wick symbol of solutions to the time-dependent Hartree-Fock equation under weaker assumptions, extending Ehrenfest-type results to a broader class of observables beyond pseudo-differential operators.

Contribution

It introduces a novel analysis of the Wick symbol in the Hartree-Fock context under less restrictive conditions, broadening the applicability of Ehrenfest theorems.

Findings

Wick symbol analysis under weaker hypotheses

Extension of Ehrenfest theorem to non-pseudo-differential observables

Broader conditions for semi-classical limits in Hartree-Fock equations

Abstract

We study the Wick symbol of a solution of the time dependent Hartree Fock equation, under weaker hypotheses than those needed for the Weyl symbol in the first paper with thesame title. With similar, we prove some kind of Ehrenfest theorem for observables that are not pseudo-differential operators.