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We analyze the method for calculation of properties of non-relativisticquantum systems based on exact diagonalization of space-discretized short-timeevolution operators. In this paper we present a detailed analysis of the errorsassociated with space discretization. Approaches using direct diagonalizationof real-space discretized Hamiltonians lead to polynomial errors indiscretization spacing $\Delta$. Here we show that the method based on thediagonalization of the short-time evolution operators leads to substantiallysmaller discretization errors, vanishing exponentially with $1/\Delta^2$. As aresult, the presented calculation scheme is particularly well suited fornumerical studies of few-body quantum systems. The analytically deriveddiscretization errors estimates are numerically shown to hold for severalmodels. In the followup paper [1] we present and analyze substantialimprovements that result from the merger of this approach with the recentlyintroduced effective-action scheme for high-precision calculation of short-timepropagation.

Properties of Quantum Systems via Diagonalization of Transition Amplitudes I: Discretization Effects