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We demonstrate the application of transition state theory to wave packetdynamics in metastable Schr\"odinger systems which are approached by means of avariational ansatz for the wave function and whose dynamics is described withinthe framework of a time-dependent variational principle. The application ofclassical transition state theory, which requires knowledge of a classicalHamilton function, is made possible by mapping the variational parameters toclassical phase space coordinates and constructing an appropriate Hamiltonianin action variables. This mapping, which is performed by a normal formexpansion of the equations of motion and an additional adaptation to the energyfunctional, as well as the requirements to the variational ansatz are discussedin detail. The applicability of the procedure is demonstrated for a cubic modelpotential for which we calculate thermal decay rates of a frozen Gaussian wavefunction. The decay rate obtained with a narrow trial wave function agreesperfectly with the results using the classical normal form of the correspondingpoint particle. The results with a broader trial wave function go even beyondthe classical approach, i.e., they agree with those using the quantum normalform. The method presented here will be applied to Bose-Einstein condensates inthe following paper [A. Junginger, M. Dorwarth, J. Main, and G. Wunner,submitted to J. Phys. A].

Transition state theory for wave packet dynamics. I. Thermal decay in metastable Schr\"odinger systems