Dynamics of uncertainties for one-dimensional semiclassical wave packets: Isochronicity, scattering, and capture

Predrag Punoševac, Sam L. Robinson

Research output: Contribution to journalArticle

Abstract

We complete our study on the uncertainties in position and momentum associated with the semiclassical Hagedorn wave packets by first filling in a technical gap in the dynamics of bound states for isochronous potentials. We then consider scattered states and show that, if the packet is reflected from the potential or transmitted through a symmetric potential, then a minimal uncertainty "initial" state cannot in general lead to a "final" state with minimal uncertainty, and we give an explicit relationship for the difference in terms of a characteristic time associated with classical trajectories. We also characterize the behavior of the uncertainty product in the case where the underlying classical dynamics lead to capture by the potential.

Original languageEnglish (US)
Article number052106
JournalJournal of Mathematical Physics
Volume60
Issue number5
DOIs
StatePublished - May 1 2019

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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