  In the Feynman-Kac[1] path integral approach the eigenvalues of a quantum
system can be computed using Wiener measure which uses Brownian particle
motion. In our previous work[2-3] on such systems we have observed that the
Wiener process numerically converges slowly for dimensions greater than two
because almost all trajectories will escape to infinity[4]. One can speed up
this process by using a Generalized Feynman-Kac (GFK) method[5] in which the
new measure associated with the trial function is stationary, so that the
convergence rate becomes much faster. We thus achieve an example of Importance
Sampling and in the present work we apply it to the Feynman-Kac(FK) path
integrals for the ground and first few excited state energies for He to speed
up the convergence rate. We calculate the path integrals using space averaging
rather than the time averaging as done in the past. The best previous
calculations from Variational computations report precisions of Hartrees,
whereas in most cases our path integral results obtained for the ground and
first excited states of He are lower than these results by about Hartrees or
more.
