Applications of an analogue of conditional Wiener integrals

Abstract

In this paper, we obtain formulas for the analogue of conditional Wiener integrals for the functional $F$ of the form $$ F(x) = \exp\Big\{ \int_{0}^{T} V(x(t)) dt \Big\}, \quad x\in C[0,T] $$ where $V: \Bbb{R} \rightarrow \Bbb{R}$ is a potential function. We then apply this formula to obtain several integration formulas for the functionals involving various potential functions which is used in quantum mechanics and other physical theories.