Symmetry groups and Gauss kernels of Schrödinger equations

doi:10.1088/1674-1056/21/2/020301

中国物理B ›› 2012, Vol. 21 ›› Issue (2): 20301-020301.doi: 10.1088/1674-1056/21/2/020301

康静¹,屈长征²

收稿日期:2011-10-10 修回日期:2011-11-29 出版日期:2012-01-30 发布日期:2012-01-30
通讯作者: 屈长征,quchangzheng@nbu.edu.cn E-mail:quchangzheng@nbu.edu.cn

Symmetry groups and Gauss kernels of Schrödinger equations

Kang Jing(康静)^a) and Qu Chang-Zheng(屈长征)^b)†

a. Department of Mathematics, Northwest University, Xi'an 710069, China;
b. Department of Mathematics, Ningbo University, Ningbo 315211, China

Received:2011-10-10 Revised:2011-11-29 Online:2012-01-30 Published:2012-01-30
Contact: Qu Chang-Zheng,quchangzheng@nbu.edu.cn E-mail:quchangzheng@nbu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China for Distinguished Young Scholars (Grant No. 10925104), the National Natural Science Foundation of China (Grant No. 11001220), and the Ph. D. Program Foundation of the Ministry of Education of China (Grant No. 20106101110008).

摘要/Abstract

Abstract: The relationship between symmetries and Gauss kernels for the Schrödinger equation iu_t=u_xx+f(x)u is established. It is shown that if the Lie point symmetries of the equation are nontrivial, a classical integral transformations of the Gauss kernels can be obtained. Then the Gauss kernels of Schrödinger equations are derived by inverting the integral transformations. Furthermore, the relationship between Gauss kernels for two equations related by an equivalence transformation is identified.

Key words: Schr?dinger equation, symmetry group, Gauss kernel, equivalence transformation

中图分类号: (Algebraic methods)

03.65.Fd

02.20.Sv (Lie algebras of Lie groups) 02.30.Jr (Partial differential equations)

康静, 屈长征. [J]. 中国物理B, 2012, 21(2): 20301-020301.

Kang Jing(康静) and Qu Chang-Zheng(屈长征) . Symmetry groups and Gauss kernels of Schrödinger equations[J]. Chin. Phys. B, 2012, 21(2): 20301-020301.

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Symmetry groups and Gauss kernels of Schrödinger equations

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