Uniform semiclassical approximations for one-dimensional fermionic systems

TL;DR

This paper develops uniform semiclassical approximations for particle and kinetic energy densities in one-dimensional fermionic systems, incorporating non-perturbative effects through advanced mathematical resummation techniques.

Contribution

It introduces a methodology that includes non-perturbative effects in semiclassical approximations for 1D fermionic systems, enhancing accuracy over previous methods.

Findings

Accurate semiclassical formulas for densities derived

Inclusion of non-perturbative effects improves approximation quality

Method applicable to bounded 1D fermionic systems

Abstract

A thorough account is given of the derivation of uniform semiclassical approximations to the particle and kinetic energy densities of N noninteracting bounded fermions in one dimension. The employed methodology allows the inclusion of non-perturbative effects via an infinite resummation of the Poisson summation formula.