QUANTUM-MECHANICAL TIME-DEVELOPMENT OPERATOR FOR THE UNIFORMLY ACCELERATED PARTICLE

We derive a useful expression for the time-development operator for qu antum wave functions, exp(<-i(H)over cap t>/(h) over bar), for the cas e of a particle subject to a constant force. We apply it, in both posi tion and momentum space, to construct wave packets that exhibit unifor m acceleration. We use these results to generate quantum wave packets corresponding to the motion of a charged particle in a uniform electri c field in two different gauges, explicitly demonstrating the change i n phase of the wave function under a gauge transformation. The more st andard description of the time dependence of accelerating wave packets using the formalism of propagators is briefly reviewed in an Appendix for comparison. (C) 1996 American Association of Physics Teachers.