  This paper is concerned with the study of Green's functions for one
dimensional diffusions with constant diffusion coefficient and linear time
inhomogeneous drift. It is well know that the whole line Green's function is
given by a Gaussian. Formulas for the Dirichlet Green's function on the half
line are only known in special cases. The main object of study in the paper is
the ratio of the Dirichlet to whole line Green's functions. Bounds, asymptotic
behavior in the limit as the diffusion coefficient vanishes, and a log
concavity result are obtained for this ratio.
