Transition from discrete to continuous time of arrival distribution for a quantum particle

We show that the Kijowski distribution for time of arrivals in the entire real line is the limiting distribution of the time of arrival distribution in a confining box as its length increases to infinity. The dynamics of the confined time of arrival eigenfunctions is also numerically investigated an...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2005-10
Main Authors: Galapon, Eric A, Delgado, F, J Gonzalo Muga, Egusquiza, Inigo
Format: Article
Language:English
Subjects:
Confining
Eigenvalues
Eigenvectors
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We show that the Kijowski distribution for time of arrivals in the entire real line is the limiting distribution of the time of arrival distribution in a confining box as its length increases to infinity. The dynamics of the confined time of arrival eigenfunctions is also numerically investigated and demonstrated that the eigenfunctions evolve to have point supports at the arrival point at their respective eigenvalues in the limit of arbitrarilly large confining lengths, giving insight into the ideal physical content of the Kijowsky distribution.
ISSN:2331-8422
DOI:10.48550/arxiv.0510081