We study the characteristic length scale of galactic halos in the Bose-Einstein condensate ( or scalar field ) dark matter model .
Considering the evolution of the density perturbation we show that the average background matter density determines the quantum Jeans mass and hence the spatial size of galaxies at a given epoch .
In this model the minimum size of galaxies increases while the minimum mass of the galaxies decreases as the universe expands .
The observed values of the mass and the size of the dwarf galaxies are successfully reproduced with the dark matter particle mass m \simeq 5 \times 10 ^ { -22 } eV .
The minimum size is about 6 \times 10 ^ { -3 } \sqrt { m / H } \lambda _ { c } and the typical rotation velocity of the dwarf galaxies is O ( \sqrt { H / m } ) c , where H is the Hubble parameter and \lambda _ { c } is the Compton wave length of the particle .
We also suggest that ultra compact dwarf galaxies are the remnants of the dwarf galaxies formed in the early universe .