  We show that a quantum deformation of quantum mechanics given in a previous
work is equivalent to quantum mechanics on a nonlinear lattice with step size
$\Delta x=~(1-q)x$. Then, based on this, we develop the basic formalism of
quantum group Schr\"{o}dinger field theory in one spatial quantum dimension,
and explicitly exhibit the $SU_{q}(2)$ covariant algebras satisfied by the
$q$-bosonic and $q$-fermionic Schr\"{o}dinger fields. We generalize this result
to an arbitrary number of fields.
