Generalized curves, geodesics, the generalized integral and implications for quantum mechanics

Abstract

The notion of relaxed trajectories, as a special class of generalized curves is introduced. This is applied to the problem of soft landing in space science. Then the notion of generalized integral is developed and applied to an integral with set-valued integrand. It is shown that the generalized integral is most appropriate for a path integral involving probabilistic motion such as the path of an elementary particle or the integral of a wildly oscillating function on an interval.