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

We show that for Hamiltonian of the form, H=c(t)∂x∂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 eβx, with β> 0. We show that there is no potential which sustains nonspreading wave packets of this kind.