Euclidean quantum mechanics in the momentum representation.

A time reversible probabilistic representation of solutions of the (Euclidean) Schrödinger equation in momentum representation is constructed using Lévy processes and bridges. Each diffusion in the position representation is associated with a jump diffusion in the momentum space. Our method can be looked upon as a rigorous version of Feynman’s path integral approach. Several examples are studied. [ABSTRACT FROM AUTHOR]