Motion of Quantum Particles in Terms of Probabilities of Paths

The Feynman path integral formalism for non-relativistic quantum mechanics is revisited. A comparison is made with cases of light propagation (Huygens' principle) and Brownian motion. The difficulties for a physical model applying Feynman's formalism are pointed out. A reformulation is proposed, where the transition probability of a particle from one space-time point to another one is the sum of probabilities of the possible paths. As an application, Born approximation for scattering is derived within the formalism, which suggests an interpretation involving the stochastic motion of a particle rather than the square of a wavelike amplitude.