Abstract
An analysis of the strict uncertainty relations for the relativistic mean position and velocity operators is given. It is shown that the variance of the physical coordinate of a relativistic particle must be greater than one half of its Compton length provided E− mc 2⪡ mc 2, E being the average value of the energy in a wave packet. However, it is always possible to create states with arbitrary small values of ΔX⪡ℏ/ mc, if E⪢ mc 2. Several explicit examples are considered.
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