  We demonstrate the application of transition state theory to wave packet
dynamics in metastable Schr\"odinger systems which are approached by means of a
variational ansatz for the wave function and whose dynamics is described within
the framework of a time-dependent variational principle. The application of
classical transition state theory, which requires knowledge of a classical
Hamilton function, is made possible by mapping the variational parameters to
classical phase space coordinates and constructing an appropriate Hamiltonian
in action variables. This mapping, which is performed by a normal form
expansion of the equations of motion and an additional adaptation to the energy
functional, as well as the requirements to the variational ansatz are discussed
in detail. The applicability of the procedure is demonstrated for a cubic model
potential for which we calculate thermal decay rates of a frozen Gaussian wave
function. The decay rate obtained with a narrow trial wave function agrees
perfectly with the results using the classical normal form of the corresponding
point particle. The results with a broader trial wave function go even beyond
the classical approach, i.e., they agree with those using the quantum normal
form. The method presented here will be applied to Bose-Einstein condensates in
the following paper [A. Junginger, M. Dorwarth, J. Main, and G. Wunner,
submitted to J. Phys. A].
