Accurate calculation of quantum and diffusion propagators in arbitrary dimensions

A new approach to calculating the dynamics and equilibrium thermodynamics of an arbitrary (quantum or stochastic) system is presented. Its key points are representing the full propagator as a product of the harmonic‐oscillator propagator with the configuration function, and expanding the configuration function (its exponent) in a power series in a given function of t. Recursion relations are obtained for the expansion coefficients which can be analytically evaluated for any number of degrees of freedom. This representation is particularly attractive for two reasons. Being structurally similar to the standard Taylorlike expansions for the propagator already known in the literature, it nevertheless shows a dramatic improvement over the latter in that it converges significantly better over a much broader range of t. Another attractive feature of the present expansion is that it is amenable to subsequent approximations. With this technique a minimal computational effort is required for constructing an improve...

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