粒子入射双δ势垒时空间分数阶薛定谔方程的解

山东大学学报(工学版) ›› 2010, Vol. 40 ›› Issue (1): 139-143.

粒子入射双δ势垒时空间分数阶薛定谔方程的解

林爱华蒋晓芸苗风明

林爱华蒋晓芸：山东大学数学学院，山东济南 250100; 林爱华苗风明：莱芜钢铁集团有限公司自动化部，山东莱芜 271104

收稿日期:2009-01-08 出版日期:2010-02-16 发布日期:2009-01-08
通讯作者: 苗风明(1983-)，男，山东泰安人，硕士研究生，主要研究方向为分数阶微积分. E-mail:mfm198363@163.com
作者简介:林爱华(1982-),女,山东泰安人,硕士,主要研究方向为分数阶微积分. E-mail:aihualin-1230@163.com
基金资助:
山东省自然科学基金资助项目(Y2007A06)

The solution to the space fractional Schro¨dinger equationwith double δ potential

Received:2009-01-08 Online:2010-02-16 Published:2009-01-08

摘要/Abstract

摘要：

给出粒子入射双δ势垒时空间分数阶薛定谔方程满足的跃变条件并给出了解,求出了在此解下相应的透射系数和反射系数,讨论了粒子发生共振透射的条件,进而

讨论了整数阶和分数阶薛定谔方程的关系。最后,文章给出了在动量表象中含有双δ势垒的空间分数阶薛定谔方程的解。

关键词: 分数阶微积分;空间分数阶薛定谔方程;双δ势垒;跃变条件;动量表象

Abstract:

The jump conditions and the solution to the fractional Schr[o¨dinger equation with a double δpotential barrierare studied. The corresponding reflection coefficient and transmission coefficient of the particle are given. Also, the relations between fractional and classical Schro¨dinger equation are discussed. The solution to the space fractional Schr[o¨dinger equation with a double δpotential barrier is obtained.

Key words: fractional calculus; space fractional Schro¨dinger equation; double δpotential barrier; jump conditions; momentum representation

林爱华蒋晓芸苗风明. 粒子入射双δ势垒时空间分数阶薛定谔方程的解[J]. 山东大学学报(工学版), 2010, 40(1): 139-143.

LIN Ai-Hua, JIANG Xiao-Yun, MIAO Feng-Ming. The solution to the space fractional Schro¨dinger equationwith double δ potential[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2010, 40(1): 139-143.

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