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We derive the main physical galaxy properties: mass, halo radius, phase spacedensity and velocity dispersion from a semiclassical gravitational approach inwhich fermionic WDM is treated quantum mechanically. They turn out to becompatible with observations. Pauli Principle implies for the fermionic DMphase-space density Q(r) = rho(r)/sigma^3(r) the quantum bound Q(r) < Km^4/hbar^3, where m is the DM particle mass, sigma(r) is the DM velocitydispersion and K is a pure number of order one which we estimate. N-body galaxysimulations produce a divergent Q(r) at r = 0 violating this quantum bound.Combining this bound with the behaviour of Q(r) from simulations, the virialand galaxy data on Q implies lower bounds on the halo radius and a minimaldistance r_{min} at which classical dynamics for DM fermions breaks down. Thisquantum bound rules out the presence of galaxy cusps for fermionic WDM, inagreement with astronomical observations, which show that the DM halos arecored. We show that compact dwarf galaxies are quantum objects supportedagainst gravity by the fermionic WDM quantum pressure. Quantum mechanicalcalculations become necessary to compute galaxy structures at kpc scales andbelow. Classical N-body simulations are not valid at scales below r_{min}. Weapply the Thomas-Fermi semiclassical approach to fermionic WDM galaxies andfind the physical magnitudes: mass, halo radius, phase-space density, velocitydispersion, consistent with observations especially for compact dwarf galaxies.Namely, fermionic WDM treated quantum mechanically, as it must be, reproducesthe sizes of the observed cores. The lightest known galaxy Willman I implies alower bound for the WDM particle mass m > 0.96 keV. These results and theobserved galaxies with halo radius > 30 pc and halo mass > 4 10^5 M_sun providefurther indication that the WDM particle mass m is in the range 1-2 keV.

Fermionic warm dark matter produces galaxy cores in the observed scales because of quantum mechanics