Chin. Phys. Lett.  2012, Vol. 29 Issue (7): 070301    DOI: 10.1088/0256-307X/29/7/070301
GENERAL |
Symmetry Groups and Gauss Kernels of the Schrödinger Equations with Potential Functions
KANG Jing1, QU Chang-Zheng2**
1Department of Mathematics, Northwest University, Xi'an 710069
2Department of Mathematics, Ningbo University, Ningbo 315211
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KANG Jing, QU Chang-Zheng 2012 Chin. Phys. Lett. 29 070301
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Abstract

We study the Gauss kernels for a class of (2+1)-dimensional linear Schrödinger equations with potential functions. The relationship between the Lie point symmetries and Gauss kernels for the Schrödinger equations is established. It is shown that a classical integral transformation of the Gauss kernel can be generated by a proper Lie point symmetry admitted by the equation. Then we can recover the Gauss kernels for the Schrödinger equations by performing the inverse integral transformation.

Received: 15 December 2011      Published: 29 July 2012
PACS:  03.65.Fd (Algebraic methods)  
  02.20.Sv (Lie algebras of Lie groups)  
  02.30.Jr (Partial differential equations)  
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https://cpl.iphy.ac.cn/10.1088/0256-307X/29/7/070301       OR      https://cpl.iphy.ac.cn/Y2012/V29/I7/070301
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KANG Jing
QU Chang-Zheng
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