  We present a time-independent quantum formalism to describe the dynamics of
molecules with permanent electric dipole moments in a two-dimensional confined
geometry such as a one-dimensional optical lattice, in the presence of an
electric field. Bose/Fermi statistics and selection rules play a crucial role
in the dynamics. As examples, we compare the dynamics of confined fermionic and
bosonic polar KRb molecules under different confinements and electric fields.
We show how chemical reactions can be suppressed, either by a "statistical
suppression" which applies for fermions at small electric fields and
confinements, or by a "potential energy suppression", which applies for both
fermions and bosons at high electric fields and confinements. We also explore
collisions that transfer molecules from one state of the confining potential to
another. Although these collisions can be significant, we show that they do not
play a role in the loss of the total number of molecules in the gas.
