Some physical applications of fractional Schroedinger equation

Journal Article · Tue Aug 15 00:00:00 EDT 2006 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2235026· OSTI ID:20860755

Xiaoyi, Guo; Mingyu, Xu ^[1]

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1. School of Mathematics and System Sciences, Shandong University, Jinan 250100 (China)

The fractional Schroedinger equation is solved for a free particle and for an infinite square potential well. The fundamental solution of the Cauchy problem for a free particle, the energy levels and the normalized wave functions of a particle in a potential well are obtained. In the barrier penetration problem, the reflection coefficient and transmission coefficient of a particle from a rectangular potential wall is determined. In the quantum scattering problem, according to the fractional Schroedinger equation, the Green's function of the Lippmann-Schwinger integral equation is given.

• OSTI ID: 20860755
• Journal Information: Journal of Mathematical Physics, Vol. 47, Issue 8; Other Information: DOI: 10.1063/1.2235026; (c) 2006 American Institute of Physics; 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
CAUCHY PROBLEM
ENERGY LEVELS
GREEN FUNCTION
LIPPMANN-SCHWINGER EQUATION
MATHEMATICAL SOLUTIONS
POTENTIALS
QUANTUM WELLS
REFLECTION
SCATTERING
SCHROEDINGER EQUATION
TRANSMISSION
WAVE FUNCTIONS