Quantum Dynamics with Gaussian Bases Defined by the Quantum Trajectories

Abstract

Development of a general approach to construction of efficient high-dimensional bases is an outstanding challenge in quantum dynamics describing large amplitude motion of molecules and fragments. A number of approaches, proposed over the years, utilize Gaussian bases whose parameters are somehow-usually by propagating classical trajectories or by solving coupled variational equations-tailored to the shape of a wave function evolving in time. In this paper we define the time-dependent Gaussian bases through an ensemble of quantum or Bohmian trajectories, known to provide a very compact representation of a wave function due to conservation of the probability density associated with each trajectory. Though the exact numerical implementation of the quantum trajectory dynamics itself is, generally, impractical, the quantum trajectories can be obtained from the wave function expanded in a basis. The resulting trajectories are used to guide compact Gaussian bases, as illustrated on several model problems.