Wigner-like expansion of the short-time propagator and deterministic numerical methods

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A systematic expansion of the short-time propagator K( x, ε, y, O) in powers of the time spacing ε and of the coordinate difference x—y is given. This expansion allows us to extend the approximation usually done in the path integral formalism to the order ε N . Taking x=y and ε=ħβ, our expansion corresponds to the Wigner expansion of the partition function. Using this improved short-time propagator in the framework of two deterministic numerical techniques, we obtain a high accuracy in numerical calculations. The method has been tested on double-well and Pöschen-Teller potentials.