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

Journal Article · Sat Mar 15 00:00:00 EDT 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4866777· OSTI ID:22250935

Dong, Jianping ^[1]

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1. Department of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China)

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.

• OSTI ID: 22250935
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
EQUATIONS
GREEN FUNCTION
QUANTUM MECHANICS
SCATTERING
SPACE
TIME DEPENDENCE
WAVE FUNCTIONS