  We have developed a variational perturbation theory based on the
Liouville-Neumann equation, which enables one to systematically compute the
perturbative correction terms to the variationally determined wave functions of
the time-dependent systems. We then apply the method to the time-independent
anharmonic oscillator, and show that the results agree with those of other
variational perturbation theories. We also show that the system has an
interesting algebraic structure at the first order correction level.
