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.
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.
KANG Jing, QU Chang-Zheng. Symmetry Groups and Gauss Kernels of the Schrödinger Equations with Potential Functions[J]. 中国物理快报, 2012, 29(7): 70301-070301.
KANG Jing, QU Chang-Zheng. Symmetry Groups and Gauss Kernels of the Schrödinger Equations with Potential Functions. Chin. Phys. Lett., 2012, 29(7): 70301-070301.
2012, Vol. 29 
