Thermal gaussian wave packets

Abstract

The notion of a thermal wave packet and the inferred spatial probability distribution are elucidated at the example of freely moving particles. Particle localisation and the use of localised Gaussian wave packets to describe a thermal state of the freely moving particle are critically assessed.

GRAPHICAL ABSTRACT

Keywords:

• Thermal states
• quantum formalism
• quantum dynamics
• Gaussian wave packets

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 According to Resolution 1 of the 26th Conference of Weights and Measures (Comptes Rendus des séances de la vingt-sixième Conférence Générale des Poids et Mesures. Résolution 1, Annexe 3, BIPM, 2019), as of 20 Mai 2019 the Boltzmann and the Planck constants have the fixed values $k_{\mathrm{B}}=1.380649{10}^{-23}\mathrm{J}/\mathrm{K}$ and $h=6.62607015{10}^{-34}\mathrm{Js}$, respectively.

Additional information

Funding

This work is supported financially by the Université de Strasbourg and CNRS. It benefits from the the ANR grant under project QDDA.