  For configurational space of arbitrary dimension a strict form of the
uncertainty principle has been obtained, which takes into account the
dependence of inequality limit on the effective number of pure states present
in given statistical mixture. It is shown that in a state with minimal
uncertainty the density operators eigenfunctions coincide with the stationary
wavefunctions of a multidimensional harmonic oscillator. The mixed state
obtained has a permutational symmetry which is typical for a system of
identical bosons.
