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Non-equilibrium path integral methods for computing quantum free energydifferences are applied to a quantum particle trapped in a harmonic well ofuniformly changing strength with the purpose of establishing the convergenceproperties of the work distribution and free energy as the number of degrees offreedom M in the regularized path integrals goes to infinity. The workdistribution is found to converge when M tends to infinity regardless of theswitching speed, leading to finite results for the free energy difference whenthe Jarzynski non-equilibrium work relation or the Crooks fluctuation relationare used. The nature of the convergence depends on the regularization method.For the Fourier method, the convergence of the free energy difference and workdistribution go as 1/M, while both quantities converge as 1/M^2 when the beadregularization procedure is used. The implications of these results to moregeneral systems are discussed.

Quantum free energy differences from non-equilibrium path integrals: II. Convergence properties for the harmonic oscillator