  In phase space, we analytically obtain the characteristic functions (CFs) of
a forced harmonic oscillator [Talkner et al., Phys. Rev. E, 75, 050102 (2007)],
a time-dependent mass and frequency harmonic oscillator [Deffner and Lutz,
Phys. Rev. E, 77, 021128 (2008)], and coupled harmonic oscillators under
driving forces in a simple and unified way. For general quantum systems, a
numerical method that approximates the CFs to $\hbar^2$ order is proposed. We
exemplify the method with a time-dependent frequency harmonic oscillator and a
family of quantum systems with time-dependent even power-law potentials.
