  We analyze the method for calculation of properties of non-relativistic
quantum systems based on exact diagonalization of space-discretized short-time
evolution operators. In this paper we present a detailed analysis of the errors
associated with space discretization. Approaches using direct diagonalization
of real-space discretized Hamiltonians lead to polynomial errors in
discretization spacing $\Delta$. Here we show that the method based on the
diagonalization of the short-time evolution operators leads to substantially
smaller discretization errors, vanishing exponentially with $1/\Delta^2$. As a
result, the presented calculation scheme is particularly well suited for
numerical studies of few-body quantum systems. The analytically derived
discretization errors estimates are numerically shown to hold for several
models. In the followup paper [1] we present and analyze substantial
improvements that result from the merger of this approach with the recently
introduced effective-action scheme for high-precision calculation of short-time
propagation.
