  The Schwartz kernel of the multiplication operation on a quantum torus is
shown to be the distributional boundary value of a classical multivariate theta
function. The kernel satisfies a Schr\"odinger equation in which the role of
time is played by the deformation parameter $\hbar$ and the role of the
hamiltonian by a Poisson structure. At least in some special cases, the kernel
can be written as a sum of products of single-variable theta functions.
