  For closed quantum systems driven away from equilibrium, work is often
defined in terms of projective measurements of initial and final energies. This
definition leads to statistical distributions of work that satisfy
nonequilibrium work and fluctuation relations. While this two-point measurement
definition of quantum work can be justified heuristically by appeal to the
first law of thermodynamics, its relationship to the classical definition of
work has not been carefully examined. In this paper we employ semiclassical
methods, combined with numerical simulations of a driven quartic oscillator, to
study the correspondence between classical and quantal definitions of work in
systems with one degree of freedom. We find that a semiclassical work
distribution, built from classical trajectories that connect the initial and
final energies, provides an excellent approximation to the quantum work
distribution when the trajectories are assigned suitable phases and are allowed
to interfere. Neglecting the interferences between trajectories reduces the
distribution to that of the corresponding classical process. Hence, in the
semiclassical limit, the quantum work distribution converges to the classical
distribution, decorated by a quantum interference pattern. We also derive the
form of the quantum work distribution at the boundary between classically
allowed and forbidden regions, where this distribution tunnels into the
forbidden region. Our results clarify how the correspondence principle applies
in the context of quantum and classical work distributions, and contribute to
the understanding of work and nonequilibrium work relations in the quantum
regime.
