Analytical solution for 3D stationary Schrodinger equation: implementation of Huygens' principle for matter waves

被引：16

作者：

Eleuch, Hichem ^{[1
,2
,3
]}

Rostovtsev, Yuri V. ^{[4
]}

机构：

[1] Texas A&M Univ, Inst Quantum Sci & Engn, College Stn, TX 77843 USA

[2] Texas A&M Univ, Dept Phys & Astron, College Stn, TX 77843 USA

[3] Princeton Univ, Appl Phys & Mat Sci Grp, Princeton, NJ 08544 USA

[4] Univ N Texas, Dept Phys, Denton, TX 76203 USA

来源：

JOURNAL OF MODERN OPTICS | 2010年 / 57卷 / 19期

关键词：

Schrodinger equation; analytical solution; FREQUENCY; MECHANICS;

D O I：

10.1080/09500340.2010.514069

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

We have found an analytical solution of the 3D stationary Schrodinger equation for any arbitrary potential. The solution has been obtained by transforming the Schrodinger equation to the generalized Ricatti equation, and it has the form of Huygens' principle for matter waves. We have shown that the solution is more accurate than the JWKB approximation. We discuss possible applications of the solution to molecular dynamics and dynamics of charges in nanostructures.

引用

页码：1877 / 1881

页数：5

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