Fermionic Phonons: Exact Analytic Results and Quantum Statistical Mechanics for a One Dimensional Harmonic Crystal
Quantum Physics
2021-08-30 v3 Statistical Mechanics
Chemical Physics
Abstract
Analytic expressions for the energy eigenvalues and eigenfunctions of a one-dimensional harmonic crystal are obtained. The average energy and density profiles are obtained numerically as a function of temperature. A surprisingly large number of energy levels (eg.\ 5,000 for 4 particles) are required for reliable results at even moderate temperatures.
Keywords
Cite
@article{arxiv.1903.06866,
title = {Fermionic Phonons: Exact Analytic Results and Quantum Statistical Mechanics for a One Dimensional Harmonic Crystal},
author = {Phil Attard},
journal= {arXiv preprint arXiv:1903.06866},
year = {2021}
}
Comments
9 pages, 5 sections, 5 figures. Total = 19. Erroneous wave function symmetrization results now removed