Infinite-dimensional Schrodinger equations with polynomial potentials and Feynman path integrals

A class of polynomial potentials for which infinite dimensional Schrödinger equations have solutions that can be represented in terms of sequential Feynman path integrals in the configuration space is studied. Cauchy problem for the Schrödinger equations in terms of limits of sequences of integral over Cartesian powers of the configuration or phase space of the corresponding classical Hamiltonian system is presented. The limits coincides with the sequential Feynman path integrals in the configuration space. Path integrals in the configuration space are used in the study. Theoritical analysis proves that the sequential Feynman integrals exist if the integrands are exponentials of certain polynomials, and the exponentials with polynomial potentials satisfy the conditions of the theorem.