  We investigate the dependence of the center-of-mass tomogram of a system with
many degrees of freedom $N$ on the Planck constant $\hbar $. It is shown that
to use the central limit theorem under taking the limit $N\to +\infty $ one
should keep the energy of the system to be constant. In the case, the resulting
distribution is Gaussian if the initial distribution is a product of
independent excited states of a quantum oscillator or even and odd coherent
states either. Then, if one turns the Planck constant $\hbar \to 0$ we get
$\delta $-function associated with the distribution concentrated in zero with
the probability equal to one.
