In recent years, we have developed a method for solving both the time-<i>independent</i> and time-<i>dependent </i>Schrödinger equations based on the von Neumann lattice of phase space Gaussians. The method, which we call PvB (periodic von Neumann with biorthogonal exchange) allows the tailoring of quantum calculations to the underlying classical phase space structure while retaining the accuracy of the Fourier grid basis. Formally the method defeats exponential scaling with dimensionality. I will present results for polyatomics obtained using the PvB method and compare with two other methods: a pruned, multidimensional coordinate DVR (discrete variable representation) and a pruned projected version of the Weylet approach of Poirier. Preliminary studies incorporating the pruned PvB and pruned DVR methods into an MCTDH (multiconfiguration time-dependent Hartree) framework will be presented.

Phase space vs. coordinate space approaches for overcoming exponential scaling in large quantum calculations

253rd National Meeting (2017)

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