  We argue that a very large class of quantum pure states of isolated
macroscopic bodies have sharply peaked energy distributions, with their width
relative to the average scaling between $\sim N^{-1}$ and $\sim N^{-1/2}$, with
$N \gg 1$, the number of atoms conforming the body. Those states are dense
superpositions of energy eigenstates within arbitrary finite or infinite energy
intervals that decay sufficiently fast. The sharpness of the energy
distribution implies that closed systems in those states are {\it
microcanonical} in the sense that only energy eigenstates very near to the mean
energy contribute to their thermodynamic evolution. Since thermodynamics
accurately describes processes of macroscopic bodies and requires that closed
systems have constant energy, our claim is that these pure states are typical
of macroscopic systems. The main assumption beneath the energy sharpness is
that the isolated body can reach thermal equilibrium if left unaltered. We
argue that such a self-sharpness of the energy in macroscopic bodies indicates
that the First Law of Thermodynamics is statistical in character.
