Symmetry groups and gauss kernels of the Schroedinger equations with potential functions

We study the Gauss kernels for a class of (2+1)-dimensional linear Schroedinger equations with potential functions. The relationship between the Lie point symmetries and Gauss kernels for the Schroedinger 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 Schroedinger equations by performing the inverse integral transformation. (authors)