  The purpose of this article is to expand the number of examples for which the
complex Green operator, that is, the fundamental solution to the Kohn
Laplacian, can be computed. We use the Lie group structure of quadric
submanifolds of $\mathbb C^n\times\mathbb C^m$ and the group Fourier transform
to reduce the $\Box_b$ equation to ones that can be solved using modified
Hermite functions. We use Mehler's formula and investigate 1) quadric
hypersurfaces, where the eigenvalues of the Levi form are not identical
(including possibly zero eigenvalues), and 2) the canonical quadrics in
$\mathbb C^4$ of codimension two.
