Quantum trajectory calculations for bipolar wavepacket dynamics in one dimension

Quantum trajectory methods (QTMs) hold great promise as a potential means of obtaining dynamical insight and computational scaling similar to classical trajectory simulations but in an exact quantum dynamical context. To date, the development of QTMs has been stymied by the "node problem"-highly nonclassical and numerically unstable trajectories that arise when the wavepacket density ψ 2 exhibits substantial interference oscillations. In a recent paper, however [B. Poirier, J. Chem. Phys. 128, 164115 (2008)], a "bipolar decomposition," ψ= ψ+ + ψ-, was introduced for one-dimensional (1D) wavepacket dynamics calculations such that the component densities ψ± 2 are slowly varying and otherwise interference-free, even when ψ 2 itself is highly oscillatory. The bipolar approach is thus ideally suited to a QTM implementation, as is demonstrated explicitly in this paper. Two model 1D benchmark systems exhibiting substantial interference are considered-one with more "quantum" system parameters and the other more classical-like. For the latter, more challenging application, synthetic QTM results are obtained and found to be extremely accurate, as compared to a corresponding fixed-grid calculation. Ramifications of the bipolar QTM approach for the classical limit and also for multidimensional applications, are discussed.