  We study the time dependent potential energy $W(t)=U(x(0)) - U(x(t))$ of a
particle diffusing in a one dimensional random force field (the Sinai model).
Using the real space renormalization group method (RSRG), we obtain the exact
large time limit of the probability distribution of the scaling variable
$w=W(t)/(T \ln t)$. This distribution exhibits a {\it nonanalytic} behaviour at
$w=1$. These results are extended to a small non-zero applied field. Using the
constrained path integral method, we moreover compute the joint distribution of
energy $W(t)$ and position $x(t)$ at time $t$. In presence of a reflecting
boundary at the starting point, with possibly some drift in the + direction,
the RSRG very simply yields the one time and aging two-time behavior of this
joint probability. It exhibits differences in behaviour compared to the
unbounded motion, such as analyticity. Relations with some magnetization
distributions in the 1D spin glass are discussed.
