The general potential V(x, t) in which Airy wave packets remain nonspreadingChyi-Lung Lin, Te-Chih Hsiung and Meng-Jie Huang
Department of Physics, Soochow University - Taipei, Taiwan, 111, ROC
received 6 June 2008; accepted in final form 13 June 2008; published August 2008
published online 1 July 2008
We show that for Hamiltonian of the form, H = c(t)+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 , with . We show that there is no potential which sustains nonspreading wave packets of this kind.
03.65.-w - Quantum mechanics.
03.65.Ge - Solutions of wave equations: bound states.
© EPLA 2008