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

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 expr...

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Bibliographic Details
Published in:Applied mathematics and computation 2011-06, Vol.217 (20), p.7966-7974
Main Authors: Zhukovsky, K.V., Dattoli, G.
Format: Article
Language:English
Subjects:
Airy packet
Analogies
Evolution
Exponential operator
Fokker–Plank
Mathematical analysis
Mathematical models
Propagation
Schroedinger equation
Schrödinger equations
Spreading
Transforms
Wave packets
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Summary: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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.02.088