Abstract
We develop a variational method for constructing the effective Hamiltonian that best propagates the state of a system, based on the minimization of a temporal error functional. As an illustrative example the procedure is used to derive the effective Hamiltonian in the time-dependent self-consistent-field method. The present variational approach is particularly useful to build the best effective Hamiltonian that is a linear combination of the generators of a Lie algebra. We explicitly consider systems having classical analogs with many degrees of freedom and calculate transition probabilities for a simple semiclassical model of the collinear collision between an atom and a diatomic molecule. We show that our variational approach is more general and accurate than the widely used local harmonic approximation.
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