https://doi.org/10.1140/epjs/s11734-023-00920-7
Regular Article
Mean square displacement of a free quantum particle on the basis of thermal Gaussian wave packets
Laboratoire de Chimie Quantique, Institut de Chimie de Strasbourg, UMR 7177 CNRS/Université de Strasbourg, CS 90032, 4, rue Blaise Pascal, 67081, Strasbourg, France
b
roberto.marquardt@unistra.fr
Received:
9
January
2023
Accepted:
2
July
2023
Published online:
7
August
2023
The mean square displacement 
of the position x of a free particle of mass m is evaluated quantum mechanically in terms of thermal Gaussian wave packets (Marquardt in Mol Phys 119(17-18): e1974110, https://doi.org/10.1080/00268976.2021.1974110, 2021). Such states represent a particle at thermal equilibrium. The approach allows us to address the evaluation of the mean square displacement in the continuum as well as under periodic boundary conditions. In the latter case, an analytical expression is obtained which is identical to the expression obtained on the basis of plane waves (Marquardt in Mol Phys 19(17-18): e1971315, https://doi.org/10.1080/00268976.2021.1971315, 2021). Results are discussed with respect to the quantum mechanical representation of observables related to the mean square displacement of particles.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
