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arXiv · 1903.06866

Fermionic Phonons: Exact Analytic Results and Quantum Statistical Mechanics for a One Dimensional Harmonic Crystal

Phil Attard
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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.

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Phil Attard. 2021-08-27. Fermionic Phonons: Exact Analytic Results and Quantum Statistical Mechanics for a One Dimensional Harmonic Crystal. https://arxiv.org/abs/1903.06866

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