Path integral analysis for Gaussian beam propagation over non-penetrable obstacles

The path integral analysis has been used to examine the propagation of a Gaussian beam in two cases. First in free space and second in a space with a non-penetrable obstacle, placed parallel to the direction of propagation. Full analytical equations have been given in both cases and results have been taken in the same spatial coordinates in order to facilitate comparisons. No numerical instabilities have been observed and the method seems to be quite tractable and easily extended in spaces with more that one obstacle.