COMBINATORIAL APPROACH TO FEYNMAN PATH INTEGRATION

Combinatorial relations can be used to convert the non relativistic ti me-sliced Feynman path integral into perturbation expansions. These me thods reveal that when the time interval is sliced into N increments, each order of perturbation theory sustains an error O(1/square-root N) . In this way we provide exact path integral results for the following potentials: delta-function comb, finite well, tunnelling barrier, and a generalized exponential cusp. For the tunnelling barrier it is seen how the celebrated (- 1) reflection factor arises in the limit of inf inite barrier height. The one-dimensional Coulomb problem is solved as a limiting case of the exponential cusp. In addition, for power poten tials we indicate how this path integral approach yields sometimes div ergent, nevertheless asymptotic perturbation expansions.