Mean square displacement of a free quantum particle in a thermal state
Abstract
The mean square displacement (x(t)-x(0))2 of the position x of a free particle of mass m at thermal equilibrium is evaluated quantum mechanically. An analytical expression is obtained which shows an initial quadratic increase of the mean square displacement with time and later on a linear growth, with the slope /m, quite at variance with the result from classical statistical mechanics. Results are discussed in relation to observables from helium scattering or spin-echo experiments, and their possible interpretation in terms of the classical and quantum mechanical expression for the mean square displacement of an essentially free particle.
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