On Derivation of the Poisson-Boltzmann Equation

TL;DR

This paper derives the nanoscopic linearized Poisson-Boltzmann equation from the microscopic reduced Hartree-Fock equation, linking microscopic quantum models to macroscopic electrostatic descriptions.

Contribution

It provides a rigorous derivation of the Poisson-Boltzmann equation starting from quantum mechanical principles, bridging microscopic and macroscopic models.

Findings

Derivation of the linearized Poisson-Boltzmann equation from microscopic models

Establishment of a theoretical connection between Hartree-Fock and electrostatic potential equations

Framework for analyzing electrostatics in nanoscopic systems

Abstract

Starting from the microscopic reduced Hartree-Fock equation, we derive the nanoscopic linearized Poisson-Boltzmann equation for the electrostatic potential associated with the electron density.