Symmetry Groups and Gauss Kernels of the Schrödinger Equations with Potential Functions

doi:10.1088/0256-307X/29/7/070301

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-Zheng^2**

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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	KANG Jing
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