  We propose that the ultralight dark matter (ULDM) model, in which dark matter
particles have a tiny mass of $m=O(10^{-22})eV$, has characteristic scales for
physical quantities of observed galaxies such as mass, size, acceleration, mass
flux, and angular momentum from quantum mechanics. The typical angular momentum
per dark matter particle is $\hbar$ and the typical physical quantities are
functions of specific angular momentum $\hbar/m$ and average background density
of the particles. If we use the Compton wavelength instead for the length
scale, we can obtain bounds for these physical quantities. For example, there
is an upper bound for acceleration of ULDM dominated objects, $a_c={c^3
m}/{\hbar}$. We suggest that the physical scales of galaxies depend on the time
of their formation and that these characteristic scales are related to some
mysteries of observed galaxies. Future observations from the James Webb Space
Telescope and NANOGrav can provide evidences for the presence and evolution of
these scales.
