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Title: Scattering problems in the fractional quantum mechanics governed by the 2D space-fractional Schrödinger equation

The 2D space-fractional Schrödinger equation in the time-independent and time-dependent cases for the scattering problems in the fractional quantum mechanics is studied. We define the Green's functions for the two cases and give the mathematical expression of them in infinite series form and in terms of some special functions. The asymptotic formulas of the Green's functions are also given, and applied to get the approximate wave functions for the fractional quantum scattering problems. These results contain those in the standard (integer) quantum mechanics as special cases, and can be applied to study the complex quantum systems.
Authors:
 [1]
  1. Department of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China)
Publication Date:
OSTI Identifier:
22250935
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; EQUATIONS; GREEN FUNCTION; QUANTUM MECHANICS; SCATTERING; SPACE; TIME DEPENDENCE; WAVE FUNCTIONS