Some physical applications of fractional Schrodinger equation

被引：240

作者：

Guo, Xiaoyi ^{[1
]}

Xu, Mingyu ^{[1
]}

机构：

[1] Shandong Univ, Sch Math & Syst Sci, Jinan 250100, Peoples R China

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2006年 / 47卷 / 08期

基金：

中国国家自然科学基金;

关键词：

D O I：

10.1063/1.2235026

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The fractional Schrodinger 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 Schrodinger equation, the Green's function of the Lippmann-Schwinger integral equation is given. (c) 2006 American Institute of Physics.

引用

页数：9

共 13 条

[1]

[Anonymous], 1982, SCATTERING THEORY WA, DOI DOI 10.1007/978-3-642-88128-2

[2]

FEYNMAN RP, 1965, QUANTUM MECH PATH IN

[3] FOX FUNCTION REPRESENTATION OF NON-DEBYE RELAXATION PROCESSES [J].

GLOCKLE, WG ;

NONNENMACHER, TF .

JOURNAL OF STATISTICAL PHYSICS, 1993, 71 (3-4) :741-757

[4]

JOACHIN CJ, 1983, QUANTUM COLLISION TH

[5] Fractals and quantum mechanics [J].

Laskin, N .

CHAOS, 2000, 10 (04) :780-790

[6] Fractional quantum mechanics [J].

Laskin, N .

PHYSICAL REVIEW E, 2000, 62 (03) :3135-3145

[7] Fractional Schrodinger equation [J].

Laskin, N .

PHYSICAL REVIEW E, 2002, 66 (05) :7-056108

[8] Fractional quantum mechanics and Levy path integrals [J].

Laskin, N .

PHYSICS LETTERS A, 2000, 268 (4-6) :298-305

[9]

LASKIN N, QUANTPH0504106

[10]

Mandelbrot BB., 1977, FRACTAL GEOMETRY NAT

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