Quantum dynamics using a discretized coherent state representation: An adaptive phase space method

We introduce a discretized coherent state representation (DCSR) for quantum dynamics. Expansion of a wave function in the nonorthogonal slightly overcomplete set is made with an identity operator computed using an iterative refinement method. Calculating the inverse of the overlap matrix is not necessary. The result is an accurate and efficient representation, where you only put basis functions in the region of phase space where the wave function is nonvanishing. Compared to traditional spatial grid methods, fewer grid points are needed. The DCSR can be viewed as an application of the Weyl-Heisenberg frame and extends it into a useful computational method. A scheme for fully quantum mechanical propagation is constructed and applied to the realistic problem of highly excited vibration in the heavy diatomic molecule Rb-2. Compared to split-operator propagation in a conventional spatial grid, an order of magnitude longer time steps can be taken and fewer grid points are needed. The computational effort scales linearly with the number of basis functions. Nonreflecting boundary conditions are a natural property of the representation and is illustrated in a model of predissociation. (C) 2001 American Institute of Physics.