Mean square displacement of a free quantum particle on the basis of thermal Gaussian wave packets

The mean square displacement ⟨( x(t)-x(0)) ^2⟩ _ 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.