We present observations of molecular gas made with the 15 m James Clark Max
well Telescope toward the sites of OH (1720 MHz) masers in three supernova
remnants: W28, W44, and 3C 391. Maps made in the (CO)-C-12 J = 3-2 line rev
eal that the OH masers are preferentially located along the edges of thin f
ilaments or clumps of molecular gas. There is a strong correlation between
the morphology of the molecular gas and the relativistic gas traced by sync
hrotron emission at centimeter wavelengths. Broad CO line widths (Delta V =
30-50 km s(-1)) are seen along these gaseous ridges, while narrow lines ar
e seen off the ridges. The ratio of H2CO line strengths is used to determin
e temperatures in the broad-line gas of 80 K, and the (CO)-C-13 J = 3-2 col
umn density suggests densities of 10(4)-10(5) cm(-3). These observations su
pport the hypothesis that the OH (1720 MHz) masers originate in postshock g
as, heated by the passage of a supernova remnant shock through dense molecu
lar gas. From the observational constraints on the density, velocity, and m
agnetic held, we examine the physical properties of the shock and discuss t
he shock production of OH. These OH (1720 MHz) masers are useful "signposts
" that point to the most promising locations to study supernova remnant/mol
ecular cloud interactions.