Evolution of non-spreading Airy wavepackets in time dependent linear potentials

K.V. Zhukovsky, G. Dattoli

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

We report on the use of the algebraic methods to obtain the explicit form of the solution of the Schrödinger equation with a linear potential. We consider the case of the explicitly time dependent Hamiltonian and formulate the general conditions that allow for the solutions to be found that are expressed in terms of Airy functions, yielding non spreading wave packets. The relevant physical meaning of these solutions is analyzed and the examples of their applications are given. The role, played by the Airy transform and its relevance to the problems, involving linear potentials is discussed. Eventually, we present a thorough discussion on the analogy between the Airy and the Gauss-Weierstrass transform, often employed in the solutions of the heat type equations. © 2011 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)7966 - 7974
Number of pages9
JournalApplied Mathematics and Computation
Volume217
Issue number20
DOIs
Publication statusPublished - 15 Jun 2011
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Computational Mathematics

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