Symmetry groups and Gauss kernels of Schrödinger equations

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

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.

Keywords: Schr?dinger equation symmetry group Gauss kernel equivalence transformation

Received: 10 October 2011
Revised: 29 November 2011
Accepted manuscript online:

PACS:	03.65.Fd	(Algebraic methods)
	02.20.Sv	(Lie algebras of Lie groups)
	02.30.Jr	(Partial differential equations)

Fund: 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).

Corresponding Authors: Qu Chang-Zheng,quchangzheng@nbu.edu.cn
E-mail: quchangzheng@nbu.edu.cn

Cite this article:

Kang Jing(康静) and Qu Chang-Zheng(屈长征) Symmetry groups and Gauss kernels of Schrödinger equations 2012 Chin. Phys. B 21 020301

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