  Motivated by the very recent observations of hidden charm pentaquarks
$P_c(4312)^+$, $P_c(4440)^+$ and $P_c(4457)^+$ of the LHCb Collaboration, we
systematically study the spectra of the doubly-heavy (with or without
charm/bottom numbers) pentaquarks and tetraquarks in non-relativistic
constituent quark model. The model independent variational method is employed
to solve the Schr\"odinger equation, where the test functions adopted are
symmetric for the light quarks. In our study, the $P_c(4312)^+$ may be assigned
as the ground state with spin-parity $\frac{1}{2}^-$ or $\frac{3}{2}^-$, while
the $P_c(4440)^+$ and $P_c(4457)^+$ may be assigned as the excited states with
$\frac{1}{2}^-$, which might all belong to the sextet with $s_{c\bar{c}}=1$ and
$s_\ell=\frac{3}{2}$. It is notable that our working framework is quite similar
to that of Hydrogen molecule, but with different potential structure. We also
classify these pentaquarks and tetraquarks in light of the heavy quark symmetry
and their decay properties are analyzed. Several promising channels for the
observation of doubly-heavy pentaquarks and doubly-heavy tetraquarks in
experiment are proposed.
