Time-development operator method in quantum mechanics

We discuss the time-development operator method in quantum mechanics. The e quivalence of this method and the usual method of expansion in terms of ene rgy eigenfunctions discussed in textbooks is pointed out. As examples of ca ses of time-dependent Hamiltonians, we discuss the time development of a Ga ussian wave packet for a charged particle subject to a time-dependent elect ric field using an operator differential equation. We also consider a spin in a time-dependent operator. (C) 2001 American Association of Physics Teac hers.