Quantum mechanical time-development operator for the uniformly accelerated particle

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Abstract

We derive a useful expression for the time-development operator for quantum wave functions, exp(-iĤt/ℏ), for the case of a particle subject to a constant force. We apply it, in both position and momentum space, to construct wave packets that exhibit uniform acceleration. We use these results to generate quantum wave packets corresponding to the motion of a charged particle in a uniform electric field in two different gauges, explicitly demonstrating the change in phase of the wave function under a gauge transformation. The more standard description of the time dependence of accelerating wave packets using the formalism of propagators is briefly reviewed in an Appendix for comparison.

Original languageEnglish (US)
Pages (from-to)803-808
Number of pages6
JournalAmerican Journal of Physics
Volume64
Issue number6
DOIs
StatePublished - Jun 1996

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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