Some physical applications of fractional Schrödinger equation

2006/08/01 by Xiaoyi Guo, Mingyu Xu · 11 citations
Physics and Astronomy · Mathematics · #Quantum Mechanics and Non-Hermitian Physics #Fractional Differential Equations Solutions #Quantum chaos and dynamical systems

paper · doi:10.1063/1.2235026

Abstract

The fractional Schrödinger 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 Schrödinger equation, the Green’s function of the Lippmann-Schwinger integral equation is given.

Citations

• The Fractal Geometry of Nature
• Time fractional Schrödinger equation

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• Quantum tunneling from a new type of generalized Smith-Volterra-Cantor potential
• Uniqueness of the fractional derivative definition
• Stabilization of single- and multi-peak solitons in the fractional nonlinear Schroedinger equation with a trapping potential
• A structure-preserving Fourier pseudo-spectral linearly implicit scheme for the space-fractional nonlinear Schrödinger equation
• The impact of memory effect on space fractional strong quantum couplers with tunable decay behavior and its numerical simulation. [europepmc]
• Experimental realisations of the fractional Schrödinger equation in the temporal domain. [europepmc]
• Quantum Information Entropy for a Hyperbolic Double Well Potential in the Fractional Schrödinger Equation. [europepmc]
• A split-step finite element method for the space-fractional Schrödinger equation in two dimensions. [europepmc]

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• On the nonlocality of the fractional Schrödinger equation
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