  We investigate quantum corrections to the classical work characteristic
function (CF) as a semiclassical approximation to the full quantum work CF. In
addition to explicitly establishing the quantum-classical correspondence of the
Feynman-Kac formula, we find that these quantum corrections must be in even
powers of $\hbar$. Exact formulas of the lowest corrections ($\hbar^2$) are
proposed, and their physical origins are clarified. We calculate the work CFs
for a forced harmonic oscillator and a forced quartic oscillator respectively
to illustrate our results.
