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| Variational approaches to quantum systems are a powerful framework for the efficient calculation of quantum dynamics. Therein, the original wave function is replaced by an appropriate trial wave function depending on a set of variational parameters, and the Schr\"{o}dinger equation is approximately solved by applying a time-dependent variational principle. The latter defines a noncanonical Hamiltonian system, for which Darboux's theorem guarantees the local existence of canonical coordinates.
In this talk, I will discuss how a normal form expansion in the variational space can be used to systematically construct such canonical coordinates in a natural way. The procedure has the advantage that the coordinates constructed are action-angle-variables in which the system becomes especially simple. As an application, a transition state theory for wave packet dynamics is presented. The treatment of quantum reaction dynamics is demonstrated for a model potential within the linear Schr\"{o}dinger theory, and for Bose-Einstein condensates as nonlinear Schr\"{o}dinger systems. |
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