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Through the use of the time-ordered perturbation expansion, an operator equation for the time-dependent perturbation problem, of the same form as occurs in the time-independent problem, is generated. Thus, a variational method can be used to study the time-dependent case as well as the time-independent case. This variational method is used to recover the Dirac expansion as an example of a solution in series form, and it is also used to develop a simple (approximate) analytic solution as an example of a solution in closed form.
Robert Yaris (1963) studied this question.