In a previous work [A. B. Weglein, Phys. Rev. A 17, 1810 (1978)], an optimization method to approximate solutions to the time-dependent Schr"odinger equation proposed by Chang and Rapp was further developed. We show that, if correct in a mathematical sense, it leads to results which are physically inadequate.
Approximate solutions to the time-dependent Schr\"odinger equation can be sought in terms of time-dependent parameters. In this work, a reasonable definition of the "best" values for these parameters is given by requiring that the time integral of the deviation of the approximate solution from the exact solution be minimized. A procedure for specifically evaluating the parameters to optimize the approximate solution is given in terms of equations analogous to Hamilton's equations of classical mechanics, which produce a minimum-deviation integral in analogy to Hamilton's principle. A comparison of this technique with previous approaches is made, both in terms of general principles, and in terms of a simple hypothetical example of a system subjected to a time-dependent perturbation.