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Deriving uniform semiclassical approximations for one-dimensional fermionic systems.

Raphael F Ribeiro¹, Kieron Burke²

¹Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA.

The Journal of Chemical Physics

|October 12, 2018

Summary

This summary is machine-generated.

This study derives uniform semiclassical approximations for particle and kinetic energy densities in one-dimensional systems. It incorporates non-perturbative quantum effects like tunneling and oscillations for bounded fermions.

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Area of Science:

Quantum mechanics
Statistical mechanics
Condensed matter physics

Background:

Understanding the behavior of quantum systems is crucial in physics.
Semiclassical approximations offer a bridge between classical and quantum mechanics.
Fermionic systems exhibit unique properties due to the Pauli exclusion principle.

Purpose of the Study:

To derive uniform semiclassical approximations for particle and kinetic energy densities.
To include non-perturbative quantum effects in these approximations.
To analyze the behavior and relationship of these densities.

Main Methods:

Derivation of uniform semiclassical approximations.
Application of the Poisson summation formula with infinite resummation.
Analysis of non-perturbative quantum effects (tunneling, quantum oscillations).

Main Results:

Complete derivation of uniform semiclassical approximations for particle and kinetic energy densities.
Inclusion of tunneling and quantum oscillations through infinite resummation.
Exploration of the analytic behavior and physical meaning of the derived approximations.

Conclusions:

The derived approximations provide a comprehensive description of fermionic systems.
Non-perturbative quantum effects are successfully integrated into the semiclassical framework.
The study clarifies the interplay between kinetic energy and particle densities in one dimension.