  While historically many quantum mechanical simulations of molecular dynamics
have relied on the Born-Oppenheimer approximation to separate electronic and
nuclear behavior, recently a lot of interest has arisen towards quantum effects
in nuclear dynamics as well. Due to the computational difficulty of solving the
Schroedinger equation in full, these effects are often treated with approximate
quasi-classical methods.
  In this paper we present a new algorithm to tackle these problems, using an
extension to the Many Interacting Worlds approach to quantum mechanics. This
technique uses a kernel function to rebuild the probability density and
therefore, at a difference with the approximation presented in the original
paper, can be naturally extended to n-dimensional systems. This opens up the
possibility of performing quantum ground state searches with steepest descent
methods as well as real time quantum molecular dynamics simulations.
  The behavior of the algorithm is studied in different potentials and numbers
of dimensions and compared both to the original approach and to exact
Schroedinger equation solutions whenever possible.
