Issue
EPL
Volume 83, Number 3, August 2008
Article Number 30002
Number of page(s) 4
Section General
DOI http://dx.doi.org/10.1209/0295-5075/83/30002
Published online 01 July 2008
EPL, 83 (2008) 30002
DOI: 10.1209/0295-5075/83/30002

The general potential V(x, t) in which Airy wave packets remain nonspreading

Chyi-Lung Lin, Te-Chih Hsiung and Meng-Jie Huang

Department of Physics, Soochow University - Taipei, Taiwan, 111, ROC

cllin@mail.scu.edu.tw

received 6 June 2008; accepted in final form 13 June 2008; published August 2008
published online 1 July 2008

Abstract
We show that for Hamiltonian of the form, H = c(t)$\partial _{x}\partial _{x}$+V(x, t), the general potential V(x, t) for which Airy packets remain nonspreading under time evolution can only be of the form V(x, t) = p(t)x+q(t), where p(t) and q(t) are real functions. We derive rules for constructing nonspreading Airy packets from this general potential. We also consider normalizable packets obtained from Airy packet times a converging factor, such as $e^{\beta x}$, with $\beta >
0$. We show that there is no potential which sustains nonspreading wave packets of this kind.

PACS
03.65.-w - Quantum mechanics.
03.65.Ge - Solutions of wave equations: bound states.

© EPLA 2008