  With Spitzer IRS we have obtained sensitive low-resolution spectroscopy from
5 to 35 microns for six supernova remnants (SNRs) that show evidence of shocked
molecular gas: Kes 69, 3C 396, Kes 17, G346.6-0.2, G348.5-0.0 and G349.7+0.2.
Bright, pure-rotational lines of molecular hydrogen are detected at the shock
front in all remnants, indicative of radiative cooling from shocks interacting
with dense clouds. We find the excitation of H2 S(0)-S(7) lines in these SNRs
requires two non-dissociative shock components: a slow, 10 km/s C- shock
through clumps of density 10^6 cm^-3, and a faster, 40-70 km/s C- shock through
a medium of density 10^4 cm^-3. The ortho-to-para ratio for molecular hydrogen
in the warm shocked gas is typically found to be much less than the LTE value,
suggesting that these SNRs are propagating into cold quiescent clouds.
Additionally a total of thirteen atomic fine-structure transitions of Ar+,
Ar++, Fe+, Ne+, Ne++, S++, and Si+ are detected. The ionic emitting regions are
spatially segregated from the molecular emitting regions within the IRS slits.
The presence of ionic lines with high appearance potential requires the
presence of much faster, dissociative shocks through a lower density medium.
The IRS slits are sufficiently wide to include regions outside the SNR which
permits emission from diffuse gas around the remnants to be separated from the
shocked emission. We find the diffuse molecular hydrogen gas projected outside
the SNR is excited to a temperature of 100 to 300 K with a warm gas fraction of
0.5 to 15 percent along the line of sight.
