Symmetry groups and Gauss kernels of Schrödinger equations |
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Authors: | Kang Jing and Qu Chang-Zheng |
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Affiliation: | Department of Mathematics, Northwest University, Xián 710069, China;Department of Mathematics, Ningbo University, Ningbo 315211, China |
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Abstract: | The relationship between symmetries and Gauss kernels for the Schrödinger equation iut=uxx+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. |
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Keywords: | Schrö dinger equation symmetry group Gauss kernel equivalence transformation |
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