  We show that Wigner-Leggett-Caldeira equation for Wigner phase space
distribution function which describes the quantum Brownian motion of a particle
in a force field in a high temerature, Ohmic environment can be identified as a
semiclassical version of Kramers' equation. Based on an expansion in powers of
$\hbar$ we solve this equation to calculate the semiclassical correction to
Kramers' rate.
