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

Fingerprint

Wave Packet
wave packets
Scattering
Uncertainty
scattering
Bound States
Momentum
trajectories
Trajectory
momentum
products

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Dynamics of uncertainties for one-dimensional semiclassical wave packets : Isochronicity, scattering, and capture. / Punoševac, Predrag; Robinson, Sam L.

In: Journal of Mathematical Physics, Vol. 60, No. 5, 052106, 01.05.2019.

Research output: Contribution to journalArticle

@article{7a231450f679434ba51f42cd89a5dbc7,
title = "Dynamics of uncertainties for one-dimensional semiclassical wave packets: Isochronicity, scattering, and capture",
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.",
author = "Predrag Punoševac and Robinson, {Sam L}",
year = "2019",
month = "5",
day = "1",
doi = "10.1063/1.5096954",
language = "English (US)",
volume = "60",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics Publising LLC",
number = "5",

}

TY - JOUR

T1 - Dynamics of uncertainties for one-dimensional semiclassical wave packets

T2 - Isochronicity, scattering, and capture

AU - Punoševac, Predrag

AU - Robinson, Sam L

PY - 2019/5/1

Y1 - 2019/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85066148680&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066148680&partnerID=8YFLogxK

U2 - 10.1063/1.5096954

DO - 10.1063/1.5096954

M3 - Article

VL - 60

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 5

M1 - 052106

ER -