  In recent years efficient algorithms have been developed for the numerical
computation of relativistic single-particle path integrals in quantum field
theory. Here, we adapt this "worldline Monte Carlo" approach to the standard
problem of the numerical approximation of the non-relativistic path integral,
resulting in a formalism whose characteristic feature is the fast,
non-recursive generation of an ensemble of trajectories that is independent of
the potential, and thus universally applicable. The numerical implementation
discretises the trajectories with respect to their time parametrisation but
maintains a continuous spatial domain. In the case of singular potentials, the
discretised action gets adapted to the singularity through a "smoothing"
procedure. We show for a variety of examples (the harmonic oscillator in
various dimensions, the modified P\"oschl-Teller potential, delta-function
potentials, the Coulomb and Yukawa potentials) that the method allows one to
obtain fast and reliable estimates for the Euclidean propagator and use them in
a certain time window suitable for extracting the ground state energy. As an
aside, we apply it for studying the classical limit where nearly classical
trajectories are expected to dominate in the path integral. We expect the
advances made here to be useful also in the relativistic case.
