Time dependent solutions for a fractional Schrödinger equation with delta potentials

We investigate, for an arbitrary initial condition, the time dependent solutions for a fractional Schrödinger equation in the presence of delta potentials by using the Green function approach. The solutions obtained show an anomalous spreading asymptotically characterized by a power-law behavior, wh...

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Bibliographic Details
Published in:Journal of mathematical physics 2013-08, Vol.54 (8), p.1
Main Authors: Lenzi, E. K., Ribeiro, H. V., dos Santos, M. A. F., Rossato, R., Mendes, R. S.
Format: Article
Language:English
Subjects:
Asymptotic methods
Asymptotic properties
Deltas
Green's functions
Initial conditions
Mathematical analysis
Operators
Physics
Schrodinger equation
Schroedinger equation
Spreading
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Summary:We investigate, for an arbitrary initial condition, the time dependent solutions for a fractional Schrödinger equation in the presence of delta potentials by using the Green function approach. The solutions obtained show an anomalous spreading asymptotically characterized by a power-law behavior, which is governed by the order of the fractional spatial operator present in the Schrödinger equation.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4819253