On the relation between momentum uncertainty and thermal wavelength

Abstract

For quantum particles in a Boltzmann state, we derive an inequality between momentum uncertainty $\Delta p$ and thermal de Broglie wavelength ${\lambda }_{\mathrm{th}}$, expressed as $\Delta p\ge \sqrt{2\pi }\hslash /{\lambda }_{\mathrm{th}}$, as a corollary of the Boltzmann lower bound for the Heisenberg uncertainty product proposed in the previous work [EPL, 143, 20001 (2023)]

arXiv comment4 pages, 1 figure